tag:blogger.com,1999:blog-37490797403724150012024-03-13T01:12:47.174-07:00BacklinksJokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.comBlogger684125tag:blogger.com,1999:blog-3749079740372415001.post-67147410971606867162023-04-16T00:00:00.000-07:002023-04-20T12:27:38.693-07:00Python and Casio fx-4000P: Transmission and Deviation Angles - Prism<p><span style="font-family: arial; font-size: medium;"><b>Python and Casio fx-4000P: Transmission and Deviation Angles - Prism</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><i><b>Celebrating 12 Years in the Blogopshere! Thank you to my readers, subscribers, and everyone who has stopped by during the years! </b></i></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Today's program calculates the transmission and deviation angles passing through a prism. The refractive index of the prism is determined by the material it is made of. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG6XLJZsbP3HzQBAoKrsZpaAaO9B2NkEptes6EESC4g7BgqURLMNqD7sKLIi7W541oRbg2YNd7JF-7XaQlzsF6tcyyRpvne44EbVTCj9P3mkGnin13Mo7sH2nrQC3T_pIyyNo5IYzkL13tZuHP_qZ0qpT7a8yUz5DP81CHFpDx6-p2_txB0SumRpZ3/s631/prism%20diagram.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="631" data-original-width="604" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG6XLJZsbP3HzQBAoKrsZpaAaO9B2NkEptes6EESC4g7BgqURLMNqD7sKLIi7W541oRbg2YNd7JF-7XaQlzsF6tcyyRpvne44EbVTCj9P3mkGnin13Mo7sH2nrQC3T_pIyyNo5IYzkL13tZuHP_qZ0qpT7a8yUz5DP81CHFpDx6-p2_txB0SumRpZ3/w612-h640/prism%20diagram.jpg" width="612" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Formulas Used for the transmission and deviation angles, respectively:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">θt = arcsin( α * √(n^2 - sin^2 θi) - sin θi * cos α)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">δ = θi + θt - α</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: large;">The Python program calculates for prisms made of acrylic</span><span style="font-family: arial; font-size: large;">, glass, fluorite</span><span style="font-family: arial; font-size: large;">, and plastic. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Python Script: prism.py</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Program Notes:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. The angle mode in Python is always radian angle mode. Conversions between degrees and radians are necessary on this code.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. This code was programmed with a Casio fx-9750GIII in the Python app. I could have used the degrees and radians functions, however, they were not present in the calculator's catalog. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. I used a While loop and initialized the choice variable k as -1 to prevent the user from choosing anything from picking outside the range 0-3. This simulates the Menu command in Casio graphing calculator programming.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">4. The refractive indices are average and approximate. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">5. To make everything fit on the screen, the new line escape character, \n, is used. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Code:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">from math import *</span></p><p><span style="font-family: courier; font-size: medium;"># radians mode</span></p><p><span style="font-family: courier; font-size: medium;">print("Enter in Degrees")</span></p><p><span style="font-family: courier; font-size: medium;">i=float(input("Incidence Angle? \n"))</span></p><p><span style="font-family: courier; font-size: medium;">a=float(input("Top Angle? \n"))</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># convert to radians</span></p><p><span style="font-family: courier; font-size: medium;">ir=i*pi/180</span></p><p><span style="font-family: courier; font-size: medium;">ar=a*pi/180</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># choice of material</span></p><p><span style="font-family: courier; font-size: medium;"># refractive index</span></p><p><span style="font-family: courier; font-size: medium;">ls=[1.4905,1.52,1.433,1.58]</span></p><p><span style="font-family: courier; font-size: medium;">k=-1</span></p><p><span style="font-family: courier; font-size: medium;">while k<0 or k>3:</span></p><p><span style="font-family: courier; font-size: medium;"> print("Select Material")</span></p><p><span style="font-family: courier; font-size: medium;"> print("0. Acrylic")</span></p><p><span style="font-family: courier; font-size: medium;"> print("1. Glass")</span></p><p><span style="font-family: courier; font-size: medium;"> print("2. Fluorite")</span></p><p><span style="font-family: courier; font-size: medium;"> print("3. Plastic")</span></p><p><span style="font-family: courier; font-size: medium;"> k=int(input())</span></p><p><span style="font-family: courier; font-size: medium;">n=ls[k]</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># calculation</span></p><p><span style="font-family: courier; font-size: medium;">t=asin(sin(ar)*sqrt(n**2-sin(ir)**2)-sin(ir)*cos(ar))</span></p><p><span style="font-family: courier; font-size: medium;">d=ir+t-ar</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># convert to degrees</span></p><p><span style="font-family: courier; font-size: medium;">td=t*180/pi</span></p><p><span style="font-family: courier; font-size: medium;">dd=d*180/pi</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># results</span></p><p><span style="font-family: courier; font-size: medium;">print("Results are in Degrees")</span></p><p><span style="font-family: courier; font-size: medium;">print("Transmission Angle: \n"+str(td))</span></p><p><span style="font-family: courier; font-size: medium;">print("Deviation: \n"+str(dd))</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Casio fx-4000P Program: Prism</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Notes:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. Variables used:</span></p><p><span style="font-family: arial; font-size: medium;">I = incidence angle</span></p><p><span style="font-family: arial; font-size: medium;">A = top angle of the prism</span></p><p><span style="font-family: arial; font-size: medium;">N = refractive index, must be entered manually</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. Outputs:</span></p><p><span style="font-family: arial; font-size: medium;">Transmission Angle (T)</span></p><p><span style="font-family: arial; font-size: medium;">Deviation Angle (D)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Code:</span></p><p><span style="font-family: arial; font-size: medium;">(59 steps)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Deg :</span></p><p><span style="font-family: courier; font-size: medium;">"I": ?→ I:</span></p><p><span style="font-family: courier; font-size: medium;">"A": ?→A:</span></p><p><span style="font-family: courier; font-size: medium;">"N": ?→N:</span></p><p><span style="font-family: courier; font-size: medium;">sin⁻¹ ( sin A × √( N² - (sin I)²) - sin I × cos A) → T ◢</span></p><p><span style="font-family: courier; font-size: medium;">I + T - A → D</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I = incidence angle</span></p><p><span style="font-family: arial; font-size: medium;">A = top angle of the prism</span></p><p><span style="font-family: arial; font-size: medium;">T = Transmission Angle</span></p><p><span style="font-family: arial; font-size: medium;">D = Deviation Angle</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. I = 50°, A = 60°, Glass (1.52)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">T ≈ 48.932708276°</span></p><p><span style="font-family: arial; font-size: medium;">D ≈ 38.932708276°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. I = 10°, A = 45°, Plastic (1.58)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">T ≈ 80.99437617°</span></p><p><span style="font-family: arial; font-size: medium;">D ≈ 45.99437617°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. I = 33°, A = 25°, Acrylic (1.4905)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">T ≈ 5.32137979°</span></p><p><span style="font-family: arial; font-size: medium;">I ≈ 13.32137979°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">4. I = 17°, A = 40°, Fluorite (1.433)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">T ≈ 42.66957975°</span></p><p><span style="font-family: arial; font-size: medium;">I ≈ 19.66957975°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Source</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><span style="font-family: arial;">Woan, Graham. </span><u style="font-family: arial;">The Cambridge Handbook of Physics Formulas</u><span style="font-family: arial;"> Cambridge</span><span style="font-family: arial;"> University Press. Cambridge, New York. 2003 edition</span></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Here is to many more years, </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-10313100456240159932023-04-15T08:11:00.000-07:002023-04-20T12:26:09.935-07:00Urban Sketching Weekend ・津田沼でのスケッチイベントを終えて振り返るHong KongのスケッチャーRob SketchermanとBen Lukが、Urban Sketchers Japan とinternationalなイベントができないか、という話をUSk Japanの仲間でアクティブに活動してくれているMomokoさんに持ちかけたのがきっかけで、話が動き出したのが昨年の12月かそこら。Momokoさんが彼女の地元の習志野でなら、文化交流に前向きにイベントをする手伝いをしてくれる黒澤さんご夫妻(Nomdecocoa)の協力でやれると思うので、引き受けた、との寝耳に水発言。え、そうなんだ、と思ったものの、以前から海外組に日本でイベントをやってほしいとの声を聞かされていたもののグループ内では話がまとまらないままズルズルと鎖国していたのもあり、ここはやる気とスキルがある彼女が引っ張ってくれるなら、みんなで協力しながらやってみようと、手探りのイベント企画が始まったのでした。<br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZCuXVeSK-WHtCapDiArhp2kMjekIfuy5E_4m8ivz8tzs2_Ul9Og1OiABzzrjykRGVyTcHqvCaDCTufBRCcbQjVBIzkWqaDX03mrYt-118bvZPhKkTBtIO16G-TWP_Xjkso2uhqzFAI5F65dRiZdfEPi4srCREh7hAoJmMtRGkjlzdod2f1U9HaUUs/s1600/IMG_0612.HEIC" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" data-original-height="3024" data-original-width="4032" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZCuXVeSK-WHtCapDiArhp2kMjekIfuy5E_4m8ivz8tzs2_Ul9Og1OiABzzrjykRGVyTcHqvCaDCTufBRCcbQjVBIzkWqaDX03mrYt-118bvZPhKkTBtIO16G-TWP_Xjkso2uhqzFAI5F65dRiZdfEPi4srCREh7hAoJmMtRGkjlzdod2f1U9HaUUs/s1600/IMG_0612.HEIC"/></a></div><br /><br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-8w8nEhhZq9Am6mDUqtgNCTSuFqo4feO7wyGZPfxI8qxX8Lp13woZuZznzo6dHqOYzGkTS0llY4qhRDe-9CQDrb5ceThEU7VgAFqa3fOs_z1PlebQyZt-pOjUhBaLoJcnLJUksTbEt--JNF2e0FFJ1SdKQyiH6dJvz9hP6HpgYF3p68ZbJuutHvev/s1920/instagram%20banner-1.png" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" height="400" data-original-height="1920" data-original-width="1080" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-8w8nEhhZq9Am6mDUqtgNCTSuFqo4feO7wyGZPfxI8qxX8Lp13woZuZznzo6dHqOYzGkTS0llY4qhRDe-9CQDrb5ceThEU7VgAFqa3fOs_z1PlebQyZt-pOjUhBaLoJcnLJUksTbEt--JNF2e0FFJ1SdKQyiH6dJvz9hP6HpgYF3p68ZbJuutHvev/s400/instagram%20banner-1.png"/></a></div><br />場所は習志野。集まる会場探し、スケッチのワークショップやdemoの出来そうな場所の下見に加え、Benはフードスケッチのワークショップをしたいので、みんなで入り浸って料理を作るところも見られ、食事を囲んでスケッチできる日本の料理を出す店がないかというハードルの高いリクエストをしてきた。(そんなお店があるのかの交渉もなされた後に、結局のところMichiyaという風情ある場所をお借りして、そこにてリクエストされた料理を料理人の方に来ていただきケータリング、セッティングをしてもらうというなんとも贅沢で素敵な方法に行き着いたのもmomokoさんと習志野組の皆さんの熱意ある尽力の賜物で。)<br /><br />2日間のイベントにするにはプログラムをどう組んで、値段はどのくらいがいいのか?どうやって代金を回収して、チェックインはどういった方法がいいのか。ボランティアが欲しいけれど、では誰に何が頼めるのか?3月中ごろあたりまでは中国からの飛行機の運行数が制限されていて、そもそも飛行機が飛べるのか?インストラクターが到着できなかったらどうなる?万一の時の代替案は?インストラクターが習志野で泊まるホテル探しと予約に、ついでに参加者で遠方から来る人の宿泊施設の案内はすべき?毎日がそういった個々の事柄についてのチャット(HK組との英語での会話あり、USk Japanのコアメンバー間でのすり合わせあり)の連続で、(実際に一つ一つをよく解決していけたものだと)実際に動いていたのはMomokoさんでしたが、その会話には加わっていた自分はこれはイベント終わる頃には腸内ポリープができちゃうかも、と胃の痛む日々を過ごしていました。自分は海外でのUSk Symposiumは度々参加していたものの、こちらでどこまでいわゆるnormに近づけられるのか、この場所でのオリジナルな企画だと参加費も海外値段には到底引き上げられないだろうという話しあいを(内輪で)散々した後で、とっつきやすい値段設定に最終的にきめ、支払いも事前にNet払いのPertixを使おうと決め、(この管理もMomokoさんにお任せ)ハンドアウトの翻訳のラフや、リーフレットに載せる地図の作画などのラフを作ったり、動けることはするものの、全てにおいて不慣れなことだらけ。しかも当初はRobのワークショップやdemoでは自分が通訳もするか、の流れだったのでしたがそこにきてWeb Designのできる瞳さん、Gloverさんや通訳をしてくれるあきほさんがいてくれたので、どんどん見栄えのいいサイトができ、スポンサーもつき商品のPaint ONの提供をいただき、印刷物に関してもNaokoさんの助けで綺麗な印刷がなされたり、自分は一つワークショップをするのと、スケッチウォークの説明、グッズの販売などという分担となりました。Casey Toriumiさんんもdemoを担当。グッズデザインは白川さんがやってくださいました。Atsukoさんもお土産セットのgoodie bagに直接直筆でイラストを描いたり名札制作もしてくれたり。Rafidaさんには突然カメラマンや通訳もしていただきとても助かりました。<br><br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyKQdXIb7_5OSk1dvP30Bc6tJcLn0HPMnGMokBXwwuk7BImYsGA3aUmu9Cv2IuVzW6vmB9arFqVDEg4UzJnL8cWSXVfj17nkG36KfUI18fAi62IUzCg2SVMjXP8RYCc42IvLU_-VemTeycJZGDn3Bq1pkSTo8ZlJy_jsXXECZqCRK7g4FtYKK5070L/s2512/IMG_0138.heic" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" width="400" data-original-height="1637" data-original-width="2512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyKQdXIb7_5OSk1dvP30Bc6tJcLn0HPMnGMokBXwwuk7BImYsGA3aUmu9Cv2IuVzW6vmB9arFqVDEg4UzJnL8cWSXVfj17nkG36KfUI18fAi62IUzCg2SVMjXP8RYCc42IvLU_-VemTeycJZGDn3Bq1pkSTo8ZlJy_jsXXECZqCRK7g4FtYKK5070L/s400/IMG_0138.heic"/></a></div><br /><br />不安は尽きず、地図を見てもよくわからないというアドバイスにはMomokoさんが行き方説明写真を掲載、イベント保険にも加入。桜が予定より早く開花し始まったので、散らないだろうか、散らないまでも雨になりそうじゃないかと気をもんだ前日までの日々。<br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTXQhAK16T08jeqx_o2PSLtD9u44G6cQ4SJa-q_mdrKcXThlSXLOgv8SxOFIepdl86YwKbbKPpJXvfs9vOglyy5cA163NLaENRfJdIEQ-nYuFjd_M3KzKX_dd6JBk7PQkiJPDy1qnOilRSsz3k_8xzpmmQkkxzpLatIcQsbw1zY-dnTmY1Q9NmnAb5/s3062/IMG_0532.heic" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" height="400" data-original-height="3062" data-original-width="2784" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTXQhAK16T08jeqx_o2PSLtD9u44G6cQ4SJa-q_mdrKcXThlSXLOgv8SxOFIepdl86YwKbbKPpJXvfs9vOglyy5cA163NLaENRfJdIEQ-nYuFjd_M3KzKX_dd6JBk7PQkiJPDy1qnOilRSsz3k_8xzpmmQkkxzpLatIcQsbw1zY-dnTmY1Q9NmnAb5/s400/IMG_0532.heic"/></a></div><br /><br /><br />蓋を開けたら花も咲いてる、天気も悪くない。来た人はちょっと時間に遅れたり迷ったりはあったものの、この風変わりな場所にちゃんと到着でき、何より楽しむぞの気合いが入っていて、その存在のおかげで拙い進行で始めたイベントを適度に脱力系の和やかな場に変えてくれていたのでした。<br /><br />参加数も完売ではないものの、なかなかの出席があり、リラックスできる習志野の町にスケッチャーが溶け込んで過ごすことのできた2日間でした。こんな機会がなかったら、一生の中で津田沼に行くこともなかっただろうと思うのですが、(ぶっちゃけ自分の住んでいる場所も都会でも田舎でもない普通の変哲のない所ですが)その町で朝から晩まで2日間歩き回り、お店でお昼を食べ、夜は飲み会もやり、描き、を繰り返すごとに不思議な親しみを持つことができました。なんだか親戚の家を訪れたようなちょっとしたボンドが生まれた、というか。<br /><br />とにかく全方面に感謝です、無事にイベントを終えることができました。<br /><br />HK組のインストラクターたちはその後のオークランドのシンポジウムにてさらに同様のWSをするというので、今回のイベントはその合間のリハーサル(?)的なこぢんまりとした会でしたが、彼らはまた来たいと言っています。今後このような国際的なイベントを続けてやりながら、裏方が消耗するだけでない、ウィンウィンな関係を保って、持続できるようにやれるかは今後のグループでの仲間同士の関わり方、反省と修正、まだ学ぶところがいっぱいです。<br /><br />やるよ、と言って有言実行したMomokoさんの人柄と人たらしぶり、パワーに拍手、脱帽でした。<br /><br />以前、隅田のTshirt会社社長の久米さんからこんな言葉を聞いたことがありました。<br /><br />何かを新しく始めるには「若者、よそ者、ばか者」がいると。あらま、今回文字通り3拍子揃ってましたね。<br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS4Jz2Lgt84J1LR87riCfkptRKv7TTX-MRiBu0aoCVqi6UnDijvYxWQgNbU62h7noLjE4HDA4gxC95WsVDn6J-zV2qDQCdYsBkROWyzZ5E1QOwtHM_ZVFY6OBDgfmCOVKA7qBjbEj9aPfpwhoomEk4fmhCXBBSHV6YQvqXtpZ_Vh4NeiQq8Vab8m5A/s4032/IMG_0373.HEIC" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" height="400" data-original-height="4032" data-original-width="3024" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS4Jz2Lgt84J1LR87riCfkptRKv7TTX-MRiBu0aoCVqi6UnDijvYxWQgNbU62h7noLjE4HDA4gxC95WsVDn6J-zV2qDQCdYsBkROWyzZ5E1QOwtHM_ZVFY6OBDgfmCOVKA7qBjbEj9aPfpwhoomEk4fmhCXBBSHV6YQvqXtpZ_Vh4NeiQq8Vab8m5A/s400/IMG_0373.HEIC"/></a></div><br />Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-27755088447137789632023-04-15T00:00:00.000-07:002023-04-20T12:27:39.031-07:00DM42, Free42, HP 42S: Birthday Probability Function<p><span style="font-family: arial; font-size: medium;"><b>DM42, Free42, HP 42S: Birthday Probability Function</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The Age Old Birthday Question</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">You probably have read or heard about when there is 23 random people in a room, half of the time someone shares a birthday. This is the classic birthday problem. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Consider a room with 3 people and assume a 365 day year calendar. What are are the odds that no one shares a birthday?</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For the first person, they clearly have any day of the calendar.</span></p><p><span style="font-family: arial; font-size: medium;">For the second person, they only have 364 days out of the calendar.</span></p><p><span style="font-family: arial; font-size: medium;">For the third person, they only have 363 days available.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The probability that no one shares a birthday is:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">P = 365/365 * 364/365 * 363/365</span></p><p><span style="font-family: arial; font-size: medium;">= (365 * 364 * 363) / (365^3)</span></p><p><span style="font-family: arial; font-size: medium;">≈ 0.99180</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">About 99.180% chance none of the three people share a birthday. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Note that:</span></p><p><span style="font-family: arial; font-size: medium;">365/365 * 364/365 * 363/365</span></p><p><span style="font-family: arial; font-size: medium;">= (365/365) * (365 - 1)/365 * (365 - 2)/365</span></p><p><span style="font-family: arial; font-size: medium;">= 1 * (365/365 - 1/365) * (365/365 - 2/365)</span></p><p><span style="font-family: arial; font-size: medium;">= 1 * (1 - 1/365) * (1 - 2/365)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The derivation above leads to the formula stated by Persi Diaconis and Brain Skyrms (pg. 20 from <u>Ten Great ideas About Chance</u>): </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">P = 1 * (N - 1)/C * (N - 2)/C * ... = Π( 1 - m/C, m = 1 to N-1)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">C = number of categories (examples: days in a calendar year, minutes in an hour, number of places, etc...)</span></p><p><span style="font-family: arial; font-size: medium;">N = sample population</span></p><p><span style="font-family: arial; font-size: medium;">P = probability that sample population does not share a category (examples: number of people that don't share the same birthday, number of people from a city that are not in the same location, etc...)</span></p><p><span style="font-family: arial; font-size: medium;">Π is the product function.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In our example above, C is the number of days in a 365 day calendar and N is the number of people. The program BDAY makes the product calculation.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>DM42/HP 42S/Free42/Plus42 Program: BDAY</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">N and C are prompted. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">00 { 58-Byte Prgm }</span></p><p><span style="font-family: courier; font-size: medium;">01▸LBL "BDAY"</span></p><p><span style="font-family: courier; font-size: medium;">02 "CATEGORIES?"</span></p><p><span style="font-family: courier; font-size: medium;">03 PROMPT</span></p><p><span style="font-family: courier; font-size: medium;">04 STO 02</span></p><p><span style="font-family: courier; font-size: medium;">05 1</span></p><p><span style="font-family: courier; font-size: medium;">06 STO 01</span></p><p><span style="font-family: courier; font-size: medium;">07 "N?"</span></p><p><span style="font-family: courier; font-size: medium;">08 PROMPT</span></p><p><span style="font-family: courier; font-size: medium;">09 1</span></p><p><span style="font-family: courier; font-size: medium;">10 -</span></p><p><span style="font-family: courier; font-size: medium;">11 STO 03</span></p><p><span style="font-family: courier; font-size: medium;">12▸LBL 00</span></p><p><span style="font-family: courier; font-size: medium;">13 1</span></p><p><span style="font-family: courier; font-size: medium;">14 RCL 03</span></p><p><span style="font-family: courier; font-size: medium;">15 RCL÷ 02</span></p><p><span style="font-family: courier; font-size: medium;">16 -</span></p><p><span style="font-family: courier; font-size: medium;">17 STO× 01</span></p><p><span style="font-family: courier; font-size: medium;">18 DSE 03</span></p><p><span style="font-family: courier; font-size: medium;">19 GTO 00</span></p><p><span style="font-family: courier; font-size: medium;">20 "PROB= "</span></p><p><span style="font-family: courier; font-size: medium;">21 ARCL 01</span></p><p><span style="font-family: courier; font-size: medium;">22 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">23 RCL 01</span></p><p><span style="font-family: courier; font-size: medium;">24 .END.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>A Quicker Calculation</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Gratitude to Thomas Klemm, this next program is listed here by permission.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A shorter way to calculate this probability (only limited to how large a calculator can handle numbers) is:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">P = PERM(C,N) / (C^N) = C! / ( (C - N)! * C^N )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>DM42/HP 42S/Free42/Plus42 Program: BDAYC (compact)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Enter C on the Y stack and N on the X stack before running the program.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">00 { 9-Byte Prgm }</span></p><p><span style="font-family: courier; font-size: medium;">01 RCL ST Y</span></p><p><span style="font-family: courier; font-size: medium;">02 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">03 PERM</span></p><p><span style="font-family: courier; font-size: medium;">04 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">05 LASTX</span></p><p><span style="font-family: courier; font-size: medium;">06 Y↑X</span></p><p><span style="font-family: courier; font-size: medium;">07 ÷</span></p><p><span style="font-family: courier; font-size: medium;">08 END</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. Probability that 40 people do not share a birthday (assume a 365 day calendar):</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">C = 365, N = 40</span></p><p><span style="font-family: arial; font-size: medium;">Probability: 0.10877</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Only about 10.877% chance no one in 40 people share a birthday. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. Probability that 3 cards drawn do not share the same suit:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">C = 4 (4 suits in a deck of cards), N = 3</span></p><p><span style="font-family: arial; font-size: medium;">Probability: 0.37500</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">About 37.5% chance no three cards share the same suit.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. A bowl has 50 numbered balls. 16 people draw a ball from the bowl and then places the ball back in the bowl.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">C = 50, N = 16</span></p><p><span style="font-family: arial; font-size: medium;">Probability: 0.06751</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Only about 6.751% of the time all 16 people draw different numbered balls. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sources</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Diaconis, Persi and Brian Skyrms <u>Ten Great Ideas About Chance</u> Princeton University Press: Princeton, New Jersey. 2018. ISBN 978-0-691-19639-8</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"(42S/DM42/Free42/Plus42) Birthday Probability Function" The Museum of HP Calculators. <a href="https://www.hpmuseum.org/forum/thread-19535.html" target="_blank">https://www.hpmuseum.org/forum/thread-19535.html</a>. Retrieved February 11, 2023. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This blog turns 12 tomorrow, so excited!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-44973782889769760392023-04-12T06:38:00.000-07:002023-04-20T12:27:39.274-07:00Review: Casio fx-991CW (and the lack of multi-statements)<p><span style="font-family: arial; font-size: medium;"><b>Review: Casio fx-991CW (and the lack of multi-statements)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg82v211K0ZS8hICIc0WInYEbdjQWzCsARR-oEfqvIi8O2xVBvzqYKkLNDgYSoswxMLkRliX2EG5-tbnsRaoyiX81djuIEtOr-JSdrl2GOcWYxQoT0SsJSV_9bJKvlbx3hvCWQHh_Ti_ySqMFFAMaMmkwxbsaMFKq3BZTyBqOJJj3GCMEkOgaNHK3Kz/s4624/20230401_122110.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg82v211K0ZS8hICIc0WInYEbdjQWzCsARR-oEfqvIi8O2xVBvzqYKkLNDgYSoswxMLkRliX2EG5-tbnsRaoyiX81djuIEtOr-JSdrl2GOcWYxQoT0SsJSV_9bJKvlbx3hvCWQHh_Ti_ySqMFFAMaMmkwxbsaMFKq3BZTyBqOJJj3GCMEkOgaNHK3Kz/w480-h640/20230401_122110.jpg" width="480" /></a></div><br /><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwlDzSVXmgVwT8MOwoV5QMCbKSog-HUfiBQbs_JfUJcVbCAQ3MHdHxWwvjceuwdixfPXTkFIM4jJKqyw2f3UtLufGtfHQi3doQQVC9abN8-tnH6ctfvHB5Et2TorI9zUZXZTpG-atuwI87HV2ps8Nsrtf0qtCLdlAE0kXQ8DDVZRSqKkLe7Q2UB5DS/s4624/20230401_122305.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwlDzSVXmgVwT8MOwoV5QMCbKSog-HUfiBQbs_JfUJcVbCAQ3MHdHxWwvjceuwdixfPXTkFIM4jJKqyw2f3UtLufGtfHQi3doQQVC9abN8-tnH6ctfvHB5Et2TorI9zUZXZTpG-atuwI87HV2ps8Nsrtf0qtCLdlAE0kXQ8DDVZRSqKkLe7Q2UB5DS/w480-h640/20230401_122305.jpg" width="480" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Quick Facts</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Model: fx-991CW</span></p><p><span style="font-family: arial; font-size: medium;">Company: Casio</span></p><p><span style="font-family: arial; font-size: medium;">Years: Internationally: 2022 - present, United States: April 2023 - present</span></p><p><span style="font-family: arial; font-size: medium;">Type: Scientific</span></p><p><span style="font-family: arial; font-size: medium;">Power: Solar with 1 LR44 backup battery</span></p><p><span style="font-family: arial; font-size: medium;">Display: Multiline, 4-color gray display</span></p><p><span style="font-family: arial; font-size: medium;">Original Price: $21.00 - $22.99 U.S. Dollars, varies on the specific version</span></p><p><span style="font-family: arial; font-size: medium;">Number of Variables: 9</span></p><p><span style="font-family: arial; font-size: medium;">Operating System: Algebraic</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Update on the Classwiz</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The fx-991CW is an update in Casio's Classwiz series, specifically on the 2015 fx-991EX Classwiz. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Check out my review on the fx-991EX Classwiz from November 2015 here:</span></p><p><span style="font-family: arial; font-size: medium;"><a href="http://edspi31415.blogspot.com/2015/11/casio-fx-991ex-classwiz-review.html" target="_blank">http://edspi31415.blogspot.com/2015/11/casio-fx-991ex-classwiz-review.html</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The modes on the Classwiz are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculate: the main app for mathematical calculations</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Statistics: 1 to 2 variable statistics. Regressions include:</span></p><p><span style="font-family: arial; font-size: medium;">Linear: y=a+bx</span></p><p><span style="font-family: arial; font-size: medium;">Quadratic: y=a+bx+cx^2</span></p><p><span style="font-family: arial; font-size: medium;">Logarithmic: y=a+b*ln(x)</span></p><p><span style="font-family: arial; font-size: medium;">Exponential: y=a*e^(bx)</span></p><p><span style="font-family: arial; font-size: medium;">Power I: y=a*b^x</span></p><p><span style="font-family: arial; font-size: medium;">Power II: y=a*x^b</span></p><p><span style="font-family: arial; font-size: medium;">Inverse: y=a+b/x</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Distribution: Calculations involving the binomial, normal, and Poisson. The Inverse Normal deal with the lower tail (left) probability only. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Spreadsheet: Like the fx-991EX and Casio's current graphing calculators, the fx-991CW has a spreadsheet which has a 5 x 45 cell capacity. The total memory is increased to 2,380 bytes (from 1,700 bytes on the fx-991EX). Basic spreadsheet features included are: labeling cells, sum, mean, minimum, maximum, absolute cell references ($), copy, cut, and paste. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Table: Generate a table of one function or two functions. The functions are defined as f(x) and g(x). With a QR code, you can generate a graph of these functions.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Equation: Solve linear systems, up to 4 x 4 equations. Solve polynomials, up to 4th order. Real coefficients only but complex roots are calculated. The general equation solver is moved to this mode. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Inequality: Solve inequalities up for polynomials of orders 2, 3, and 4.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Complex Number: Complex number arithmetic with polar/rectangular conversion, integer powers, real/imaginary parts, conjugate</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Base N: Integer arithmetic with Boolean logic. Instead of keys, the [FORMAT] key cycles through the four modes: Decimal, Hexadecimal, Binary, Octal. Binary integers are up to 31 bytes with 1 sign bit. We can not store or recall varaible values in this mode.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Matrix: Works with four matrices up to 4 rows and 4 columns. Functions include transpose, inverse, and determinant.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Vector: Works with 4 vectors with either 2 or 3 elements. Functions include dot product, norm, and cross product.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Ratio: Solves common ratio problems.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Math Box: This is the a new feature to the Classwiz. For the United States, the Math Box has two simulations: Dice Rolls and Coin Toss. Depending on the country, the CW may include additional features. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Emulator and Classpad.net</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Purchasing a fx-991CW came with a emulator license with ClassPad.net. The license number can be obtained using the Get Started option from the Settings menu. Use the QR code. For my calculator, the license for using ClassPad.net is seven years at no cost. However, using an emulator without first purchasing an eligible calculator will require an additional cost. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">You can find details about Classpad.net here: <a href="https://classpad.net/intl/features/" target="_blank">https://classpad.net/intl/features/</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><b>Keyboard, What is Added, and What is Subtracted</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXW9izTTRV42Cdn1omSUPG01bqlrJ3ukTP9DiGhvQBLIy6HM8ENXjYfV8cfhAp5azDZRLamwALS7ind4_N-3zIsaqRDOF_-VT0PhAV9Ld5oTvEDEPfR3jvHMvj-foyywyzMBZiBQXcmHtWtgrGanZVTG9UFUEibG7o6iRQnQETElk-t_wjBM5opfuL/s2819/keyboard%20close%20up.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1543" data-original-width="2819" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXW9izTTRV42Cdn1omSUPG01bqlrJ3ukTP9DiGhvQBLIy6HM8ENXjYfV8cfhAp5azDZRLamwALS7ind4_N-3zIsaqRDOF_-VT0PhAV9Ld5oTvEDEPfR3jvHMvj-foyywyzMBZiBQXcmHtWtgrGanZVTG9UFUEibG7o6iRQnQETElk-t_wjBM5opfuL/w400-h219/keyboard%20close%20up.jpg" width="400" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The keyboard of the fx-991CW is quite different from the previous Casio calculators. The keys are now round with a lot less labels. Most of functions are now stored in the catalog and tools. Let's go over some of these keys:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ house icon ]: [HOME]. This is where we switch the modes of the fx-991CW. There are no numerical shortcuts, so we have to arrow and scroll to select the mode we want. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ three lines ]: [SETTINGS]. The settings key replaces the SETUP key sequence. </span></p><p><span style="font-family: arial; font-size: medium;">Also note that the sub menus are selected by either pressing [ → ] or [ EXE ]. If there are radio buttons, select the option desired. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ curved arrow ]: [EXIT/EDIT]. This key, on the 2nd row, 2nd key from the left, will be used to exit menus and re-edit expressions. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ double up arrow ]/[ double down arrow ]: This key, top right of the calculator, is used to quickly scroll through menus or lists. Think of this key as the Page Up/Page Down key.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ < >x] ]/[VARIABLE]: This is the variable key.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwMiIjmGlYsew-W40pxKEylPy2s8cib32HTgJdiTFz-c8_SYf4g94wo73Iap286vK9yXCoVMD8JSl8BKjcAv2tluos7Zy1nYHZq_qvEVMPuL0cwB6SFr6pRtvIt00MohfWLiSfSysSkOpAtT0WqnDRSGSSENRq7k8UqHfK_h3lgLYjSG2KEEOQCtKa/s194/variable%20screen.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="73" data-original-width="194" height="151" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwMiIjmGlYsew-W40pxKEylPy2s8cib32HTgJdiTFz-c8_SYf4g94wo73Iap286vK9yXCoVMD8JSl8BKjcAv2tluos7Zy1nYHZq_qvEVMPuL0cwB6SFr6pRtvIt00MohfWLiSfSysSkOpAtT0WqnDRSGSSENRq7k8UqHfK_h3lgLYjSG2KEEOQCtKa/w400-h151/variable%20screen.png" width="400" /></a></div><br /><p><span style="font-family: arial; font-size: large;">Here is where we will store and edit values that are stored in each of the nine variables. This key replaces the STORE key. If we are operate in a mode that does not allow for editing or store values, there will be a lock icon with the selected variable. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To store a result:</span></p><p><span style="font-family: arial; font-size: medium;">1. Execute operation or recalling a calculated stat variable.</span></p><p><span style="font-family: arial; font-size: medium;">2. Press [VARIABLE].</span></p><p><span style="font-family: arial; font-size: medium;">3. Select variable, press [ OK ].</span></p><p><span style="font-family: arial; font-size: medium;">4. Select Store, press [ OK ].</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To edit a variable's value:</span></p><p><span style="font-family: arial; font-size: medium;">1. Press [VARIABLE].</span></p><p><span style="font-family: arial; font-size: medium;">2. Select variable, press [ OK ].</span></p><p><span style="font-family: arial; font-size: medium;">3. Select Edit, press [ OK ].</span></p><p><span style="font-family: arial; font-size: medium;">4. Enter the new value, press [ OK ].</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To recall a variable in a calculation:</span></p><p><span style="font-family: arial; font-size: medium;">1. Press [ SHIFT ].</span></p><p><span style="font-family: arial; font-size: medium;">2. Press any of the following keys to get the variable:</span></p><p><span style="font-family: arial; font-size: medium;">[ 4 ]: A</span></p><p><span style="font-family: arial; font-size: medium;">[ 5 ]: B</span></p><p><span style="font-family: arial; font-size: medium;">[ 6 ]: C</span></p><p><span style="font-family: arial; font-size: medium;">[ 1 ]: D</span></p><p><span style="font-family: arial; font-size: medium;">[ 2 ]: E</span></p><p><span style="font-family: arial; font-size: medium;">[ 3 ]: F</span></p><p><span style="font-family: arial; font-size: medium;">[ 0 ]: x</span></p><p><span style="font-family: arial; font-size: medium;">[ . ]: y</span></p><p><span style="font-family: arial; font-size: medium;">[ x10^ ]: z</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There is no ALPHA key as it was in past Casio calculators. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ f(x) ]/[FUNCTION]: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9zo07zfrhRSBjn1WKnoFUhXRsZnJjHPw-wdYCXBMxTrlubhgcyw-dvZrvJwrUxBs_U2wXcukt6mdMEggvqFtqkN4jCJNifPxcU9Xb3QFsyviBIuMbUirCmXvBadnpFuQosaSlLmaO-mOvOacG7yRyoegMi2YIrsTZtCJjkYnCYyqxmIvOhAtZtSU-/s194/function%20screen.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="73" data-original-width="194" height="151" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9zo07zfrhRSBjn1WKnoFUhXRsZnJjHPw-wdYCXBMxTrlubhgcyw-dvZrvJwrUxBs_U2wXcukt6mdMEggvqFtqkN4jCJNifPxcU9Xb3QFsyviBIuMbUirCmXvBadnpFuQosaSlLmaO-mOvOacG7yRyoegMi2YIrsTZtCJjkYnCYyqxmIvOhAtZtSU-/w400-h151/function%20screen.png" width="400" /></a></div><br /><p><span style="font-family: arial; font-size: large;">Here is where we can store and use up to two functions: f(x) and g(x). The great news is that f(x) and g(x) are no longer limited to the Table, they can be used in other modes such as Calculate. The equations f(x) and g(x) are retained while switching modes but not retained when the calculator either is turned off or the Input/Output setting is changed. A missed opportunity for the latter.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A plus is that either f(x) or g(x) can be a composite function. That is f(x) can contain g(x) or g(x) can contain f(x). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There are two ways to access the x variable: its own key [ x ] or the key sequence [ SHIFT ] [ 0 ]. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[book]/[CATALOG]: This is where all the functions and commands can be accessed. The menu order of the catalog changes depending on the mode used. Some submenus include:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Function Analysis: The calculus functions, that used to be on the keyboard, are now stored in the Function Analysis menu: derivative, integral, summation, logarithm*, log*, ln* (* also on the keyboard)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Probability: % (divides the number by 100), factorial, permutation, combination, random number, random integer</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Numeric: Absolute Value, Round Off (round the number to the Fix settings internally)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Angle/Coord/Sexa...: angle units (degrees, radians, grads, degrees minutes seconds*), polar/rectangular conversions (* also on the keyboard)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sci Constants: 47 scientific Constants</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Unit Conversions</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ three circles ]/[ TOOLS ]: The TOOLS menu changes dynamically based on the mode. For example, the Calculate mode will have an Undo function.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ FORMAT ]: Instead of the [S<=>D] key, we have the [FORMAT] key, which asks how to change the value: Standard, Decimal, Improper Fraction, Mixed Fraction, ENG (Engineering) Notation, Sexagesimal (degrees-minutes-seconds).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In Base mode, the [ FORMAT ] key toggles between the four bases (decimal, hexadecimal, binary, octal).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I did three comparison speed tests between the fx-991CW and fx-991EX here: <a href="https://www.youtube.com/watch?v=cj0Odnv0Mwk" target="_blank">https://www.youtube.com/watch?v=cj0Odnv0Mwk</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">As I understand, the fx-991CW has a faster processor than the previous fx-991EX.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Now let's talk about what is subtracted in this update. You read this correctly, several features did not make it from the fx-991EX to the fx-991CW:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The CALC feature where we could type in a formula, press [ CALC ] and have formula evaluation. I was not able to find the CALC feature on the fx-991CW.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There is no longer the independent memory M, nor the storage arithmetic functions M+ and M-. I miss this feature the most. I really wish scientific and graphing calculators in general embrace store arithmetic like Hewlett Packard and Swiss Micros.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There is no longer the ability to use multi-statement expressions, with each expression separated with a colon. Even when it was available, (1) storing results immediately terminated the expression (forcing the use of Ans and when available, PreAns to make using results in the next part possible), and (2) when replayed, the statement was broken up into separate parts. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: red; font-family: arial; font-size: medium;"><b>Addendum </b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Note (4/12/2023): I am wrong when I said that storing results in multi-statements on the fx-991EX (not the fx-991CW) is impossible. We use the equals key ([ALPHA] ( = )), as in this example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">A = 9 : B = 8 * A</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Csaba Tizedes uses the multi-statement and CALC feature on the fx-991EX to create an IF-THEN-ELSE structure. In this video Tizedes uses this structure to solve equations using the Bisection method. The IF-THEN-ELSE structure tests whether a number is positive or negative. Please take a look his video:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><a href="https://www.youtube.com/watch?v=umxScZL1V6A" style="font-family: arial; font-size: large;" target="_blank">https://www.youtube.com/watch?v=umxScZL1V6A</a></p><p><span style="font-family: arial; font-size: large;"><br /></span></p><p><span style="font-family: arial; font-size: large;">Gratitude to Csaba Tizedes, this video is shared with his permission. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Final Thoughts</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Overall, the fx-991CW is pretty solid calculator with a readable screen and a lot of features. My favorite part of the updated is the ability to use the functions f(x) and g(x) outside of the table function. I also like the catalog key and the page up/page down key.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I get that Casio is going for a simpler, non-busy keyboard. However, I prefer a separate ALPHA key, along with a STORE key: it's the most efficient way to store variables. A consequence of a non-busy keyboard is that a lot of the commands can only be accessed through menus. The ALPHA key could have freed nine keys for more common shifted keys such as x!, polar/rectangular conversions, etc. I would have liked to see a couple of customizable keys where we can store commands, which could be the shift of the multiplication and division keys. The financial calculator FC-200V has two slots to store commands.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The faster processor and the better screen are pluses. You will still get a lot for the money spent on the fx-991CW. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Caveat: However, if you want, need, or require subtracted features described above (CALC feature, independent memory, multi-statement expressions), you are better off buying the former fx-991EX or a fx-115ES Plus 2nd Edition. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Unfortunately, removing the multi-statement, Casio sapped it's algorithmic power with the fx-991CW, and it needs to come back. Furthermore, please put integer part, fraction part, and sign functions. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-25263223654003654202023-04-09T00:00:00.000-07:002023-04-20T12:27:39.520-07:00 Casio fx-9750GIII: Drawing the Unit Circle with an Angle<p><span style="font-family: arial; font-size: medium;"><b>Casio fx-9750GIII: Drawing the Unit Circle with an Angle</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><b style="font-family: arial; font-size: large;">Introduction</b></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program TRIGCIRC draws a unit circle on the left side of the screen with any angle entered. This program is an approximate simulation to the trigonometric circle application that is set to appear on future Casio non-graphing calculators in Europe, such as Belgium version of the fx-92. Link: <a href="https://tiplanet.org/forum/viewtopic.php?p=271049#p271049" target="_blank">https://tiplanet.org/forum/viewtopic.php?p=271049#p271049</a> </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program uses the full unit circle only. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Casio fx-9750GIII Program: TRIGCIRC</b></span></p><p><span style="font-family: arial; font-size: medium;">(316 bytes)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Code:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 5</span></p><p><span style="font-family: courier; font-size: medium;">ClrText</span></p><p><span style="font-family: courier; font-size: medium;">Menu "ANGLE","DEG",1,"RAD",2,"GRAD",3</span></p><p><span style="font-family: courier; font-size: medium;">Lbl 1:Deg:Goto 4</span></p><p><span style="font-family: courier; font-size: medium;">Lbl 2:Rad:Goto 4</span></p><p><span style="font-family: courier; font-size: medium;">Lbl 3:Gra:Goto 4</span></p><p><span style="font-family: courier; font-size: medium;">Lbl 4</span></p><p><span style="font-family: courier; font-size: medium;">ClrGraph</span></p><p><span style="font-family: courier; font-size: medium;">ViewWindow -1.5,5,1,-1.5,1.5,1</span></p><p><span style="font-family: courier; font-size: medium;">"ANGLE"?→A</span></p><p><span style="font-family: courier; font-size: medium;">SketchThick Circle 0,0,1</span></p><p><span style="font-family: courier; font-size: medium;">SketchThick F-Line 0,0,cos A,sin A</span></p><p><span style="font-family: courier; font-size: medium;">Text 5,70,"sin θ:"</span></p><p><span style="font-family: courier; font-size: medium;">Text 12,70,sin A</span></p><p><span style="font-family: courier; font-size: medium;">Text 19,70,"cos θ:"</span></p><p><span style="font-family: courier; font-size: medium;">Text 26,70,cos A</span></p><p><span style="font-family: courier; font-size: medium;">If cos A≠0</span></p><p><span style="font-family: courier; font-size: medium;">Then</span></p><p><span style="font-family: courier; font-size: medium;">Text 33,70,"tan θ:"</span></p><p><span style="font-family: courier; font-size: medium;">Text 40,70,tan A</span></p><p><span style="font-family: courier; font-size: medium;">IfEnd</span></p><p><span style="font-family: courier; font-size: medium;">Text 47,70,"θ:"</span></p><p><span style="font-family: courier; font-size: medium;">Text 54,70,A◢</span></p><p><span style="font-family: courier; font-size: medium;">Menu "AGAIN?","YES",5,"NO",6</span></p><p><span style="font-family: courier; font-size: medium;">Lbl 6</span></p><p><span style="font-family: courier; font-size: medium;">"END - 2023 EWS"</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Program Notes:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. Adding a display command, ◢, after a draw command like Text freezes the draw screen. Program execution continues by pressing [ EXE ].</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. The Text command works with pixels rather than Cartesian points. Line numbers range from 0 to 63, top to down. Column numbers range from 0 to 127, right to left.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. Syntax of Text: Text line number, column number, text. Text may have a string or a variable, but not both.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">4. I have a wrap-around label (Lbl 5) to let the user enter multiple angles.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">5. Due to the linear output of the programming mode, results are shown in floating point decimal approximations. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">6. tan x = sin x / cos x. If cos x = 0, then tan x is undefined. This is why the If condition is present. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Example Screenshots</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmPrbkUQ7YlnNkfXaA7IAAVAnpdoyKMvx3K1Jg57qEiaVW1QZN34o6Arv1q5fSBBHzVMdhM-Kax4YodwObE8tQdXRMRNG1zNYUk5UdKfVwNMsdQVdkmn4A0g8dfif5pw8BhCwN6d42ySs3KROTdxEDvkW3ozp7a2AhtnPvM1nx6HVfI8YBtnmNKIoP/s843/drawing%20circle%20unit%20example.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="453" data-original-width="843" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmPrbkUQ7YlnNkfXaA7IAAVAnpdoyKMvx3K1Jg57qEiaVW1QZN34o6Arv1q5fSBBHzVMdhM-Kax4YodwObE8tQdXRMRNG1zNYUk5UdKfVwNMsdQVdkmn4A0g8dfif5pw8BhCwN6d42ySs3KROTdxEDvkW3ozp7a2AhtnPvM1nx6HVfI8YBtnmNKIoP/w640-h344/drawing%20circle%20unit%20example.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I hope you find this useful and educational. Have an excellent day,</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-84386677918973577472023-04-08T19:39:00.000-07:002023-04-20T12:27:39.764-07:00New OS Update for Casio Classpad II<p><span style="font-family: arial; font-size: medium;"><b>New OS Update for Casio Classpad II</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Per TIPlanet: Casio has released a new OS version (2.01.7002). Among the changes includes the new off-screen when the Classpad is turned off with Casio's new logo "Boost Your Curiosity". </span></p><p><span style="font-family: arial; font-size: medium;">The updates do not include the Python programming language (I don't think).</span></p><p><span style="font-family: arial; font-size: medium;">The calculators included are the fx-CP400 and fx-CP500.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">TIPlanet's News Link with Downloads (in French):</span></p><p><span style="font-family: arial; font-size: medium;"><a href="https://tiplanet.org/forum/viewtopic.php?p=271577#p271577" target="_blank">https://tiplanet.org/forum/viewtopic.php?p=271577#p271577</a><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Casio's Download Resources Page:</span></p><p><span style="font-family: arial; font-size: medium;"><a href="https://edu.casio.com/download_service/en/download/index.html" target="_blank">https://edu.casio.com/download_service/en/download/index.html</a><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For those of you who celebrate, Happy Easter!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><p><br /></p>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-69528620207223571922023-04-08T00:00:00.000-07:002023-04-20T12:27:40.010-07:00HP 21S: Gompertz Curve<p><span style="font-family: arial; font-size: medium;"><b>HP 21S: Gompertz Curve</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This program fits sequential data to the Gompertz Curve:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y = c * a ^ (b ^ x)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">b = ( (S3 - S1) / (S2 - S1) ) ^ 1/m</span></p><p><span style="font-family: arial; font-size: medium;">a = e^( (S2 - S1) / b * (b - 1) / (b^m - 1)^2 )</span></p><p><span style="font-family: arial; font-size: medium;">c = e^( 1 / m * (S1 * S3 - S2^2) / (S1 + S3 - 2 * S2) )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">m = number of data points / 3</span></p><p><span style="font-family: arial; font-size: medium;">S1 = Σ ln x_i of the first tier </span></p><p><span style="font-family: arial; font-size: medium;">S2 = Σ ln x_i of the second tier</span></p><p><span style="font-family: arial; font-size: medium;">S3 = Σ ln x_i of the third tier</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">HP 21S Program Code: Gompertz Curve</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Labels:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: initialize the program</span></p><p><span style="font-family: arial; font-size: medium;">B: enter data</span></p><p><span style="font-family: arial; font-size: medium;">C: calculate b, a, c</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Registers:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">R1 = natural log of the sum of the first-third of data points</span></p><p><span style="font-family: arial; font-size: medium;">R2 = natural log of the sum of the second-third of data points</span></p><p><span style="font-family: arial; font-size: medium;">R3 = natural log of the sum of the third-third of data points</span></p><p><span style="font-family: arial; font-size: medium;">R4 = n = number of data points ÷ 3</span></p><p><span style="font-family: arial; font-size: medium;">R5 = a</span></p><p><span style="font-family: arial; font-size: medium;">R6 = b</span></p><p><span style="font-family: arial; font-size: medium;">R7 = c</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Program Code:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">step #: key code; key</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">01: 61, 41, A; LBL A</span></p><p><span style="font-family: courier; font-size: medium;">02: 51, 75; CLRG</span></p><p><span style="font-family: courier; font-size: medium;">03: 61, 26; RTN</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">04: 61, 41, b; LBL B</span></p><p><span style="font-family: courier; font-size: medium;">05: 13; LN</span></p><p><span style="font-family: courier; font-size: medium;">06: 21, 75, 1; STO+ 1</span></p><p><span style="font-family: courier; font-size: medium;">07: 26; R/S</span></p><p><span style="font-family: courier; font-size: medium;">08: 13; LN</span></p><p><span style="font-family: courier; font-size: medium;">09: 21, 75, 2; STO+ 2</span></p><p><span style="font-family: courier; font-size: medium;">10: 26; R/S</span></p><p><span style="font-family: courier; font-size: medium;">11: 13; LN</span></p><p><span style="font-family: courier; font-size: medium;">12: 21, 75, 3; STO+ 3</span></p><p><span style="font-family: courier; font-size: medium;">13: 1; 1</span></p><p><span style="font-family: courier; font-size: medium;">14: 21, 75, 4; STO+ 4</span></p><p><span style="font-family: courier; font-size: medium;">15: 22, 4; RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">16: 61, 26; RTN</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">17: 61, 41, C; LBL C</span></p><p><span style="font-family: courier; font-size: medium;">18: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">19: 22, 3; RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">20: 65; ×</span></p><p><span style="font-family: courier; font-size: medium;">21: 22, 2; RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">22: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">23: 45; ÷</span></p><p><span style="font-family: courier; font-size: medium;">24: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">25: 22, 2; RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">26: 65; -</span></p><p><span style="font-family: courier; font-size: medium;">27: 22, 1; RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">28: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">29: 74; =</span></p><p><span style="font-family: courier; font-size: medium;">30: 14; y^x</span></p><p><span style="font-family: courier; font-size: medium;">31: 22, 4; RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">32: 15; 1/x</span></p><p><span style="font-family: courier; font-size: medium;">33: 74; =</span></p><p><span style="font-family: courier; font-size: medium;">34: 21, 6; STO 6</span></p><p><span style="font-family: courier; font-size: medium;">35: 26; R/S</span></p><p><span style="font-family: courier; font-size: medium;">36: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">37: 22, 2; RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">38: 65; -</span></p><p><span style="font-family: courier; font-size: medium;">39: 22, 1; RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">40: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">41: 55; ×</span></p><p><span style="font-family: courier; font-size: medium;">42: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">43: 22, 6; RCL 6</span></p><p><span style="font-family: courier; font-size: medium;">44: 65; -</span></p><p><span style="font-family: courier; font-size: medium;">45: 1; 1</span></p><p><span style="font-family: courier; font-size: medium;">46: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">47: 45; ÷</span></p><p><span style="font-family: courier; font-size: medium;">48: 22, 6; RCL 6</span></p><p><span style="font-family: courier; font-size: medium;">49: 45; ÷</span></p><p><span style="font-family: courier; font-size: medium;">50: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">51: 22, 6; RCL 6</span></p><p><span style="font-family: courier; font-size: medium;">52: 14; y^x</span></p><p><span style="font-family: courier; font-size: medium;">53: 22, 4; RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">54: 65; -</span></p><p><span style="font-family: courier; font-size: medium;">55: 1; 1</span></p><p><span style="font-family: courier; font-size: medium;">56: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">57: 51, 11; x^2</span></p><p><span style="font-family: courier; font-size: medium;">58: 74; =</span></p><p><span style="font-family: courier; font-size: medium;">59: 12; e^x</span></p><p><span style="font-family: courier; font-size: medium;">60: 21, 5; STO 5</span></p><p><span style="font-family: courier; font-size: medium;">61: 26; R/S</span></p><p><span style="font-family: courier; font-size: medium;">62: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">63: 22, 1; RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">64: 55; ×</span></p><p><span style="font-family: courier; font-size: medium;">65: 22, 3; RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">66: 65; -</span></p><p><span style="font-family: courier; font-size: medium;">67: 22, 2; RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">68: 51, 11; x^2</span></p><p><span style="font-family: courier; font-size: medium;">69: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">70: 45; ÷</span></p><p><span style="font-family: courier; font-size: medium;">71: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">72: 22, 4; RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">73: 55; ×</span></p><p><span style="font-family: courier; font-size: medium;">74: 33; (</span></p><p><span style="font-family: courier; font-size: medium;">75: 22, 1; RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">76: 75; +</span></p><p><span style="font-family: courier; font-size: medium;">77: 22, 3; RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">78: 65; -</span></p><p><span style="font-family: courier; font-size: medium;">79: 2; 2</span></p><p><span style="font-family: courier; font-size: medium;">80: 55; ×</span></p><p><span style="font-family: courier; font-size: medium;">81: 22, 2; RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">82: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">83: 34; )</span></p><p><span style="font-family: courier; font-size: medium;">84: 74; =</span></p><p><span style="font-family: courier; font-size: medium;">85: 12; e^x</span></p><p><span style="font-family: courier; font-size: medium;">86: 21, 7; STO 7</span></p><p><span style="font-family: courier; font-size: medium;">87: 61, 26; RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Example</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Fit the following data into a Gompertz curve:</span></p><p><span style="font-family: arial; font-size: medium;">(1, 16)</span></p><p><span style="font-family: arial; font-size: medium;">(2, 18)</span></p><p><span style="font-family: arial; font-size: medium;">(3, 19)</span></p><p><span style="font-family: arial; font-size: medium;">(4, 25)</span></p><p><span style="font-family: arial; font-size: medium;">(5, 28)</span></p><p><span style="font-family: arial; font-size: medium;">(6, 29)</span></p><p><span style="font-family: arial; font-size: medium;">(7, 32)</span></p><p><span style="font-family: arial; font-size: medium;">(8, 36)</span></p><p><span style="font-family: arial; font-size: medium;">(9, 37)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">First, order the data points. Second, divide the data into three equal parts. For this example, we have 9 data points. From our example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">16, 18, 19, 25, 28, 29, 32, 36, 37</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">is divided into:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Group I: 16, 18, 19</span></p><p><span style="font-family: arial; font-size: medium;">Group II: 25, 28, 29</span></p><p><span style="font-family: arial; font-size: medium;">Group III: 32, 36, 37</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Initialize the program: XEQ A</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Enter the data:</span></p><p><span style="font-family: arial; font-size: medium;">16 XEQ B, 25 R/S, 32 R/S</span></p><p><span style="font-family: arial; font-size: medium;">18 XEQ B, 28 R/S, 36 R/S</span></p><p><span style="font-family: arial; font-size: medium;">19 XEQ B, 29 R/S, 37 R/S</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculate the parameters: XEQ C</span></p><p><span style="font-family: arial; font-size: medium;">b: 0.82711002676, R/S</span></p><p><span style="font-family: arial; font-size: medium;">a: 2.33690515E-1, R/S</span></p><p><span style="font-family: arial; font-size: medium;">c: 48.2137954914</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The Gompertz Curve is </span></p><p><span style="font-family: arial; font-size: medium;">y = 48.2137954914 * 2.33690515E-1 ^ (0.82711002676 ^ x)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Predict the 10th point:</span></p><p><span style="font-family: arial; font-size: medium;">Key strokes: RCL 6, y^x ,10, =, RCL 5, y^x, LAST, ×, RCL 7 </span></p><p><span style="font-family: arial; font-size: medium;">Result: 38.776391586</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Source</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><u>HP-37E & HP-38E/38C: Marketing and Forecasting Applications</u> Hewlett Packard. May 1979.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Until next time,</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-43914285393628857692023-04-04T00:00:00.000-07:002023-04-20T12:27:40.255-07:00April Haul<p><span style="font-family: arial; font-size: medium;"> The mathematical tools purchased in April so far...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">From the Pasadena City College Swap Meet:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A 27-slot soroban abacus, the longest abacus that I have ever seen..</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEill4qBZDMIl5tfRcGAAEFekw5m_OoPItF3oq-aXjJLDph7iPjq9GQAQbn_It2_T0pMxYdthL2_D4NNVIYxx3buIZBLJGO3e1LhUthkJZcBWw45JXI_5FiBEvCQquxOlfk_kfG94V2GfqX4KXo8Unx63G-sNuTJ_h_ez11SMnhYWbD-dFK0gTujSnvE/s4624/27%20slot%20soroban.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial; font-size: medium;"><img border="0" data-original-height="1326" data-original-width="4624" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEill4qBZDMIl5tfRcGAAEFekw5m_OoPItF3oq-aXjJLDph7iPjq9GQAQbn_It2_T0pMxYdthL2_D4NNVIYxx3buIZBLJGO3e1LhUthkJZcBWw45JXI_5FiBEvCQquxOlfk_kfG94V2GfqX4KXo8Unx63G-sNuTJ_h_ez11SMnhYWbD-dFK0gTujSnvE/w640-h184/27%20slot%20soroban.jpg" width="640" /></span></a></div><span style="font-family: arial; font-size: medium;"><br /></span><p><span style="font-family: arial; font-size: medium;">A 5 inch Frederick Post Co. No. 1444K slide rule.</span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIqeTsCIwS9nWacQWMUQbOyY_IWcJsICdtnIRo2EKGKv8VZz_sFJNENi2o2OyE6_9is7JotDWKGH-ga3pZ4ivdaNR6c_Ol8-UYOLUvH0_QTGsE0ZQGDsW8woHEhutNY2YCghfgRrio5It-LhddvxNjNCtlIxF7zR17i3Nx_UrQcR9Qu4r2K42fhhIb/s4134/slide%20rule%201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial; font-size: medium;"><img border="0" data-original-height="2064" data-original-width="4134" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIqeTsCIwS9nWacQWMUQbOyY_IWcJsICdtnIRo2EKGKv8VZz_sFJNENi2o2OyE6_9is7JotDWKGH-ga3pZ4ivdaNR6c_Ol8-UYOLUvH0_QTGsE0ZQGDsW8woHEhutNY2YCghfgRrio5It-LhddvxNjNCtlIxF7zR17i3Nx_UrQcR9Qu4r2K42fhhIb/w640-h320/slide%20rule%201.jpg" width="640" /></span></a></div><span style="font-family: arial; font-size: medium;"><br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAiSGsYTSQo6dpRT3gCAq7QUeVo7e_SRYehuXfokSP9hthB4WSs85Orr-l-0tAcy3ursQSKE0GvrNJl1gxO_nTlQfh97xafejloQ0H7FK9_N-YKSGCE_7OEVGVa7pemvUXrAZ8DzP0B2Koaz9QXNVHLDGZCckr-8ASW33k4BPK6SAP0daMyj6uU9Ip/s4027/slide%20rule%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial; font-size: medium;"><img border="0" data-original-height="1886" data-original-width="4027" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAiSGsYTSQo6dpRT3gCAq7QUeVo7e_SRYehuXfokSP9hthB4WSs85Orr-l-0tAcy3ursQSKE0GvrNJl1gxO_nTlQfh97xafejloQ0H7FK9_N-YKSGCE_7OEVGVa7pemvUXrAZ8DzP0B2Koaz9QXNVHLDGZCckr-8ASW33k4BPK6SAP0daMyj6uU9Ip/w640-h300/slide%20rule%202.jpg" width="640" /></span></a></div><span style="font-family: arial; font-size: medium;"><br /></span><p><span style="font-family: arial; font-size: medium;">Online:</span></p><p><span style="font-family: arial; font-size: medium;">Sharp EL-506TS (review to come soon)</span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijdNvZsol3MujQeCeV4f7ojculbmexKZBHzMGL5Y8dfUpQTiyEK8g6PCaXvUhx-S8GdkPG4-KP7lZAfIoxCp2MNux0eFAwsetDF4QUtQmyxCfSeCb7ISdO23R1pAxESpGgfP3Kh_uJ3pfXmb08uYnySXL6kQboUSl3OHVv9iUFUlAOroULqQIkz1uN/s4624/20230403_212232.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial; font-size: medium;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijdNvZsol3MujQeCeV4f7ojculbmexKZBHzMGL5Y8dfUpQTiyEK8g6PCaXvUhx-S8GdkPG4-KP7lZAfIoxCp2MNux0eFAwsetDF4QUtQmyxCfSeCb7ISdO23R1pAxESpGgfP3Kh_uJ3pfXmb08uYnySXL6kQboUSl3OHVv9iUFUlAOroULqQIkz1uN/w480-h640/20230403_212232.jpg" width="480" /></span></a></div><span style="font-family: arial; font-size: medium;"><br /></span><p><span style="font-family: arial; font-size: medium;">Casio fx-991CW: (See review here: <a href="http://edspi31415.blogspot.com/2023/04/review-casio-fx-991cw.html" target="_blank">http://edspi31415.blogspot.com/2023/04/review-casio-fx-991cw.html</a></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuRi_MW7KQ7jgzLOEgp0LJkqFp1wEopreOD40qimAICxaDMtp2Pl4ZyZy-cHpeBGln8IZ3o_gNfOo2Zma4hxjun_zfv-eVAuxwODyOgHebs4_s_HOPMiwEQk0Gii1xHB3JrlBWH6ZiZQY40mivQFvNlp1s_MxWkuqI67dXvVgrm4Vtv5ndeWzwteH5/s4000/20230403_212334.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial; font-size: medium;"><img border="0" data-original-height="4000" data-original-width="3000" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuRi_MW7KQ7jgzLOEgp0LJkqFp1wEopreOD40qimAICxaDMtp2Pl4ZyZy-cHpeBGln8IZ3o_gNfOo2Zma4hxjun_zfv-eVAuxwODyOgHebs4_s_HOPMiwEQk0Gii1xHB3JrlBWH6ZiZQY40mivQFvNlp1s_MxWkuqI67dXvVgrm4Vtv5ndeWzwteH5/w480-h640/20230403_212334.jpg" width="480" /></span></a></div><span style="font-family: arial; font-size: medium;"><br /></span><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial; font-size: medium;"><br /></span></div><span style="font-family: arial; font-size: medium;"><br /></span><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="background-color: white;"><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></span></p>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-77984666087708175932023-04-02T00:00:00.000-07:002023-04-20T12:27:40.501-07:00Swiss Micros DM41X: Cash Register<p><span style="font-family: arial; font-size: medium;"><b>Swiss Micros DM41X: Cash Register</b></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><b>Ready to Check Out?</b> </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Download the program here (raw file): <a href="https://drive.google.com/file/d/102ekvHr4c3shBY6RvAuAZzjj1g1ctD7L/view?usp=share_link" target="_blank">https://drive.google.com/file/d/102ekvHr4c3shBY6RvAuAZzjj1g1ctD7L/view?usp=share_link</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This program simulates a cash register. If you have an HP infrared printer like the HP 82240B (from the 1980s and 1990s), the program is set to print the results. The printer is enabled by setting flag 21. When a printer is present, flag 55 is set internally. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">When the printer flag is turned on (21):</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">AVIEW: print what ever is in the alpha register</span></p><p><span style="font-family: arial; font-size: medium;">VIEW: print the contents of a numeric register</span></p><p><span style="font-family: arial; font-size: medium;">ADV: advances the paper</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A printer is not required to run the program, unplug the Infrared Printer Module. This way the program stops when an AVIEW, VIEW, and ADV instruction displays. Press [ R/S ] to continue.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This program assumes every item entered is subject to a sales tax, which is set within the program, line 03. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>DM41X/HP41CX Program: CASHREG</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">When you are done entering the costs for items checked out, enter zero.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">01 LBL^T CASHREG</span></p><p><span style="font-family: courier; font-size: medium;">02 FIX 2</span></p><p><span style="font-family: courier; font-size: medium;">03 8.75 ← set your sales tax rate here </span></p><p><span style="font-family: courier; font-size: medium;">04 STO 02</span></p><p><span style="font-family: courier; font-size: medium;">05 0</span></p><p><span style="font-family: courier; font-size: medium;">06 STO 01</span></p><p><span style="font-family: courier; font-size: medium;">07 SF 21 ← allows the calculator to print/display</span></p><p><span style="font-family: courier; font-size: medium;">08 ^T THE STORE</span></p><p><span style="font-family: courier; font-size: medium;">09 33</span></p><p><span style="font-family: courier; font-size: medium;">10 XTOA ← ammends an exclamation point (!)</span></p><p><span style="font-family: courier; font-size: medium;">11 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">12 CLA</span></p><p><span style="font-family: courier; font-size: medium;">13 FIX 8</span></p><p><span style="font-family: courier; font-size: medium;">14 DATE</span></p><p><span style="font-family: courier; font-size: medium;">15 ADATE</span></p><p><span style="font-family: courier; font-size: medium;">16 AVIEW ← prints the date</span></p><p><span style="font-family: courier; font-size: medium;">17 CLA</span></p><p><span style="font-family: courier; font-size: medium;">18 FIX 2</span></p><p><span style="font-family: courier; font-size: medium;">19 ADV</span></p><p><span style="font-family: courier; font-size: medium;">20 LBL 00 ← main loop</span></p><p><span style="font-family: courier; font-size: medium;">21 ^T COST?</span></p><p><span style="font-family: courier; font-size: medium;">22 PROMPT</span></p><p><span style="font-family: courier; font-size: medium;">23 X=0?</span></p><p><span style="font-family: courier; font-size: medium;">24 GTO 01</span></p><p><span style="font-family: courier; font-size: medium;">25 ARCL X</span></p><p><span style="font-family: courier; font-size: medium;">26 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">27 ST+ 01</span></p><p><span style="font-family: courier; font-size: medium;">28 GTO 00</span></p><p><span style="font-family: courier; font-size: medium;">29 LBL 01</span></p><p><span style="font-family: courier; font-size: medium;">30 ^T SUBTOTAL</span></p><p><span style="font-family: courier; font-size: medium;">31 ARCL 01</span></p><p><span style="font-family: courier; font-size: medium;">32 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">33 CLA</span></p><p><span style="font-family: courier; font-size: medium;">34 ARCL 02</span></p><p><span style="font-family: courier; font-size: medium;">35 ^T |- % TAX:</span></p><p><span style="font-family: courier; font-size: medium;">36 RCL 01</span></p><p><span style="font-family: courier; font-size: medium;">37 RCL 02</span></p><p><span style="font-family: courier; font-size: medium;">38 %</span></p><p><span style="font-family: courier; font-size: medium;">39 ARCL X</span></p><p><span style="font-family: courier; font-size: medium;">40 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">41 +</span></p><p><span style="font-family: courier; font-size: medium;">42 ^T TOTAL:</span></p><p><span style="font-family: courier; font-size: medium;">43 ARCL X</span></p><p><span style="font-family: courier; font-size: medium;">44 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">45 ^T PAID:</span></p><p><span style="font-family: courier; font-size: medium;">46 PROMPT</span></p><p><span style="font-family: courier; font-size: medium;">47 ARCL X</span></p><p><span style="font-family: courier; font-size: medium;">48 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">49 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">50 -</span></p><p><span style="font-family: courier; font-size: medium;">51 ^T CHANGE:</span></p><p><span style="font-family: courier; font-size: medium;">52 ARCL X</span></p><p><span style="font-family: courier; font-size: medium;">53 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">54 END</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Example</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Checkout:</span></p><p><span style="font-family: arial; font-size: medium;">$19.99</span></p><p><span style="font-family: arial; font-size: medium;">$27.95</span></p><p><span style="font-family: arial; font-size: medium;">$28.94</span></p><p><span style="font-family: arial; font-size: medium;">Sales Tax Rate: 8.75%</span></p><p><span style="font-family: arial; font-size: medium;">Paid: $100.00</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">XEQ CASHREG</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">THE STORE</span></p><p><span style="font-family: arial; font-size: medium;">01/29/2023 ← the current date is shown here</span></p><p><span style="font-family: arial; font-size: medium;">COST? 19.99 R/S</span></p><p><span style="font-family: arial; font-size: medium;">COST? 27.95 R/S</span></p><p><span style="font-family: arial; font-size: medium;">COST? 28.94 R/S</span></p><p><span style="font-family: arial; font-size: medium;">COST? 0</span></p><p><span style="font-family: arial; font-size: medium;">SUBTOTAL: 76.88</span></p><p><span style="font-family: arial; font-size: medium;">8.75% TAX: 6.73</span></p><p><span style="font-family: arial; font-size: medium;">TOTAL: 83.61</span></p><p><span style="font-family: arial; font-size: medium;">PAID: 100 R/S</span></p><p><span style="font-family: arial; font-size: medium;">PAID: 100.00</span></p><p><span style="font-family: arial; font-size: medium;">CHANGE: 16.39</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-70774061299973694322023-04-01T00:00:00.000-07:002023-04-20T12:27:40.755-07:00 TI-84 Plus CE and Numworks: System of Linear Differential Equations (Simple System) <p><span style="font-family: arial; font-size: medium;"><b>TI-84 Plus CE and Numworks: System of Linear Differential Equations (Simple System)</b> </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Solving The System</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program presented today will solve the following system of equations:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">dx/dt = A * x(t) + B * y(t)</span></p><p><span style="font-family: arial; font-size: medium;">dy/dt = C * x(t) + D * y(t)</span></p><p><span style="font-family: arial; font-size: medium;">with initial conditions x(0) = x0 and y(0) = y0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The formulas used in the program are derived using the Laplace Transform.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">dx/dt = A * x(t) + B * y(t)</span></p><p><span style="font-family: arial; font-size: medium;">dy/dt = C * x(t) + D * y(t)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Laplace Transforms to be used:</span></p><p><span style="font-family: arial; font-size: medium;">ℒ{f(t)} = F(s)</span></p><p><span style="font-family: arial; font-size: medium;">ℒ{df/dt} = s * F(s) - f(0)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Apply the Laplace Transform transform:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">s * X(s) - x0 = A * X(s) + B * Y(s)</span></p><p><span style="font-family: arial; font-size: medium;">s * Y(s) - y0 = C * X (s) + B * Y(s)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">(s - A) * X(s) + (-B) * Y(s) = x0</span></p><p><span style="font-family: arial; font-size: medium;">(-C) * X(s) + (s - D) * Y(s) = y0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Define three matrices:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Md = [ [ s - A, -B ], [ -C, s - D ] ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where</span></p><p><span style="font-family: arial; font-size: medium;">det(Md) = s^2 - (A + D) * s + (A * D - B * C)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">which can be factored into:</span></p><p><span style="font-family: arial; font-size: medium;">(s - P) * (s - Q)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where:</span></p><p><span style="font-family: arial; font-size: medium;">P = (( A + D ) + √(( A + D)^2 - 4 * (A * D - B * C)) /2</span></p><p><span style="font-family: arial; font-size: medium;">Q = (( A + D ) - √(( A + D)^2 - 4 * (A * D - B * C)) /2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Mx = [ [ x0, -B ], [ y0, s - D ] ] </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where</span></p><p><span style="font-family: arial; font-size: medium;">det(Mx) = x0 * (s - D) + B * y0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">My = [ [ s - A, x0 ], [ - C, y0 ] ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where </span></p><p><span style="font-family: arial; font-size: medium;">det(My) = (s - A) * y0 + C * x0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Per Cramer's Rule, the solution to X(s) and Y(s) are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">X(s) = det(Mx) / det(Md)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Y(s) = det(My) / det(Md)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">What happens next depends of the roots P and Q. We're assuming that P and Q are real here but the situation applies if P and Q are complex. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b>If P ≠ Q:</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If P ≠ Q, then after simplifying and finding partial fractions:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">X(s) = ( x0 * (s - D) + B * y0 ) / ((s - P) * (s - Q)) = α / (s - P) + β / (s - Q)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where</span></p><p><span style="font-family: arial; font-size: medium;">α = ( B * y0 + (P - D) *x0) / (P - Q)</span></p><p><span style="font-family: arial; font-size: medium;">β = x0 - α</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Y(s) = ( (s - A) * y0 + C * x0 ) / ((s - P) * (s - Q)) = γ / (s - P) + δ / (s - Q)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where</span></p><p><span style="font-family: arial; font-size: medium;">γ =(C * x0 + y0 * (P - A)) / (P - Q)</span></p><p><span style="font-family: arial; font-size: medium;">δ = y0 - γ</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Applying the inverse Laplace transform:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x(t) = α * e^(P * t) + β * e^(Q * t)</span></p><p><span style="font-family: arial; font-size: medium;">y(t) = γ * e^(P * t) + δ * e^(Q * t)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b>If P = Q:</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If P = Q, then after simplifying and finding partial fractions:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">X(s) = ( x0 * (s - D) + B * y0 ) / (s - P)^2 = α / (s - P)^2 + β / (s - Q)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where</span></p><p><span style="font-family: arial; font-size: medium;">α = B * y0 + (P - D) * x0 </span></p><p><span style="font-family: arial; font-size: medium;">β = x0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Y(s) = ( (s - A) * y0 + C * x0 ) / (s - P)^2 = γ / (s - P)^2 + δ / (s - Q)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where</span></p><p><span style="font-family: arial; font-size: medium;">γ =C * x0 + y0 * (P - A)</span></p><p><span style="font-family: arial; font-size: medium;">δ = y0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Applying the inverse Laplace transform:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x(t) = α * t * e^(P * t) + β * e^(Q * t)</span></p><p><span style="font-family: arial; font-size: medium;">y(t) = γ * t * e^(P * t) + δ * e^(Q * t)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>TI-84 Plus CE Program: LINSYS1</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Download the program here: <a href="https://drive.google.com/file/d/14zYpT4xhLRGVvBNriOacIOGBpqXLWswR/view?usp=share_link" target="_blank">https://drive.google.com/file/d/14zYpT4xhLRGVvBNriOacIOGBpqXLWswR/view?usp=share_link</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Program Listing:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Radian</span></p><p><span style="font-family: courier; font-size: medium;">a+b<i><b>i</b></i></span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Disp "DX/DT=AX+BY DY/DT=CX+DY"</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A,B,C,D</span></p><p><span style="font-family: courier; font-size: medium;">Input "X0? ",M</span></p><p><span style="font-family: courier; font-size: medium;">Input "Y0? ",N</span></p><p><span style="font-family: courier; font-size: medium;">((A+D)+√((A+D)²-4*(A*D-B*C)))/2→P</span></p><p><span style="font-family: courier; font-size: medium;">((A+D)-√((A+D)²-4*(A*D-B*C)))/2→P</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">If P≠Q</span></p><p><span style="font-family: courier; font-size: medium;">Then</span></p><p><span style="font-family: courier; font-size: medium;">(B*N-D*M+P*M)/(P-Q)→R</span></p><p><span style="font-family: courier; font-size: medium;">M-R→S</span></p><p><span style="font-family: courier; font-size: medium;">(C*M-A*N+P*N)/(P-Q)→U</span></p><p><span style="font-family: courier; font-size: medium;">N-U→V</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Output(2,1,"X=Re^(PT)+Se^(QT)")</span></p><p><span style="font-family: courier; font-size: medium;">Output(3,1,"R= "+toString(R))</span></p><p><span style="font-family: courier; font-size: medium;">Output(4,1,"P= "+toString(P))</span></p><p><span style="font-family: courier; font-size: medium;">Output(5,1,"S= "+toString(S))</span></p><p><span style="font-family: courier; font-size: medium;">Output(6,1,"Q= "+toString(Q))</span></p><p><span style="font-family: courier; font-size: medium;">Pause</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Output(2,1,"Y=Ue^(PT)+Ve^(QT)")</span></p><p><span style="font-family: courier; font-size: medium;">Output(3,1,"U= "+toString(U))</span></p><p><span style="font-family: courier; font-size: medium;">Output(4,1,"P= "+toString(P))</span></p><p><span style="font-family: courier; font-size: medium;">Output(5,1,"V= "+toString(V))</span></p><p><span style="font-family: courier; font-size: medium;">Output(6,1,"Q= "+toString(Q))</span></p><p><span style="font-family: courier; font-size: medium;">Pause</span></p><p><span style="font-family: courier; font-size: medium;">Else</span></p><p><span style="font-family: courier; font-size: medium;">B*N-D*M+M*P→P</span></p><p><span style="font-family: courier; font-size: medium;">M→S</span></p><p><span style="font-family: courier; font-size: medium;">C*M-A*N+N*P→U</span></p><p><span style="font-family: courier; font-size: medium;">N→V</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Output(2,1,"X=RTe^(PT)+Se^(PT)")</span></p><p><span style="font-family: courier; font-size: medium;">Output(3,1,"R= "+toString(R))</span></p><p><span style="font-family: courier; font-size: medium;">Output(4,1,"P= "+toString(P))</span></p><p><span style="font-family: courier; font-size: medium;">Output(5,1,"S= "+toString(S))</span></p><p><span style="font-family: courier; font-size: medium;">Pause</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Output(2,1,"Y=UTe^(PT)+Ve^(PT)")</span></p><p><span style="font-family: courier; font-size: medium;">Output(3,1,"U= "+toString(U))</span></p><p><span style="font-family: courier; font-size: medium;">Output(4,1,"P= "+toString(P))</span></p><p><span style="font-family: courier; font-size: medium;">Output(5,1,"V= "+toString(V))</span></p><p><span style="font-family: courier; font-size: medium;">Pause</span></p><p><span style="font-family: courier; font-size: medium;">End</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Python: dfsys1.py</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Link from my Numworks page: <a href="https://my.numworks.com/python/ews31415/dfsys1" target="_blank">https://my.numworks.com/python/ews31415/dfsys1</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Modules: </span></p><p><span style="font-family: arial; font-size: medium;">cmath: complex math</span></p><p><span style="font-family: arial; font-size: medium;">mathplotlib.pyplot: screen plotting and text placement</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Script listing: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">from cmath import *</span></p><p><span style="font-family: courier; font-size: medium;">from matplotlib.pyplot import *</span></p><p><span style="font-family: courier; font-size: medium;"># 2023-01-28 EWS</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># parameter input</span></p><p><span style="font-family: courier; font-size: medium;">print("systems of differential\nequations")</span></p><p><span style="font-family: courier; font-size: medium;">print("dx/dt=a*x+b*y")</span></p><p><span style="font-family: courier; font-size: medium;">print("dy/dt=c*x+d*y")</span></p><p><span style="font-family: courier; font-size: medium;">a=float(input("a? "))</span></p><p><span style="font-family: courier; font-size: medium;">b=float(input("b? "))</span></p><p><span style="font-family: courier; font-size: medium;">c=float(input("c? "))</span></p><p><span style="font-family: courier; font-size: medium;">d=float(input("d? "))</span></p><p><span style="font-family: courier; font-size: medium;">m=float(input("x0? "))</span></p><p><span style="font-family: courier; font-size: medium;">n=float(input("y0? "))</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># characteristic roots</span></p><p><span style="font-family: courier; font-size: medium;">p=((a+d)+sqrt((a+d)**2-4*(a*d-b*c)))/2</span></p><p><span style="font-family: courier; font-size: medium;">q=((a+d)-sqrt((a+d)**2-4*(a*d-b*c)))/2</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># set up result screen</span></p><p><span style="font-family: courier; font-size: medium;">axis((0,10,0,10))</span></p><p><span style="font-family: courier; font-size: medium;">axis("off")</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"># determine solutions</span></p><p><span style="font-family: courier; font-size: medium;"># best used for real solutions</span></p><p><span style="font-family: courier; font-size: medium;">if p!=q:</span></p><p><span style="font-family: courier; font-size: medium;"> r=(b*n+m*(p-d))/(p-q)</span></p><p><span style="font-family: courier; font-size: medium;"> s=m-r</span></p><p><span style="font-family: courier; font-size: medium;"> u=(c*m+n*(p-a))/(p-q)</span></p><p><span style="font-family: courier; font-size: medium;"> v=n-u</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,9,"x=re**(pt)+se**(qt)")</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,8.5,"r="+str(r))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,8,"p="+str(p))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,7.5,"s="+str(s))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,7,"q="+str(q))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,6,"y=ue**(pt)+se**(vt)")</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,5.5,"u="+str(u))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,5,"p="+str(p))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,4.5,"v="+str(v))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,4,"q="+str(q))</span></p><p><span style="font-family: courier; font-size: medium;">else:</span></p><p><span style="font-family: courier; font-size: medium;"> r=(b*n+m*(p-d))</span></p><p><span style="font-family: courier; font-size: medium;"> s=m</span></p><p><span style="font-family: courier; font-size: medium;"> u=(c*m+n*(p-a))</span></p><p><span style="font-family: courier; font-size: medium;"> v=n</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,9,"x=rte**(pt)+se**(pt)")</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,8.5,"r="+str(r))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,8,"p="+str(p))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,7.5,"s="+str(s))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,6,"y=ute**(pt)+se**(vt)")</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,5.5,"u="+str(u))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,5,"p="+str(p))</span></p><p><span style="font-family: courier; font-size: medium;"> text(0,4.5,"v="+str(v))</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">show()</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">dx/dt = 3 * x(t) - 2 * y(t)</span></p><p><span style="font-family: arial; font-size: medium;">dy/dt = 2 * x(t) - 2 * y(t)</span></p><p><span style="font-family: arial; font-size: medium;">x(0) = 6, y(0) = 9</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Solutions:</span></p><p><span style="font-family: arial; font-size: medium;">x(t) = 2 * e^(2*t) + 4 * e^(-t)</span></p><p><span style="font-family: arial; font-size: medium;">y(t) = e^(2*t) + 8 * e^(-t)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">dx/dt = 3 * x(t) - 4 * y(t)</span></p><p><span style="font-family: arial; font-size: medium;">dy/dt = x(t) - y(t)</span></p><p><span style="font-family: arial; font-size: medium;">x(0) = 1, y(0) = 0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Solutions:</span></p><p><span style="font-family: arial; font-size: medium;">x(t) = 2 * t * e^(t) + e^(t)</span></p><p><span style="font-family: arial; font-size: medium;">y(t) = t * e^(t) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-60852489609565123922023-03-26T00:00:00.000-07:002023-04-20T12:27:41.001-07:00HP 32S II Statistical Formulas<p><span style="font-family: arial; font-size: medium;"><b>HP 32S II Statistical Formulas</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Statistics Formulas</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The 32S II can store formulas for evaluations, including formulas involving stat variables. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Covariance:</span></p><p><span style="font-family: courier; font-size: medium;">C = r × sx × sy</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Root Mean Square Based on X Variable Statistics:</span></p><p><span style="font-family: courier; font-size: medium;">R = SQRT( Σx^2 ÷ n )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Z-Score Based on X Variable Statistics: </span></p><p><span style="font-family: courier; font-size: medium;">Z = (X - x-bar) ÷ sx</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Accessing Stat variables:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r: [ right shift ] [ LN ] (L.R.) [ y^x ] (r)</span></p><p><span style="font-family: arial; font-size: medium;">sx: [ right shift ] [ 1/x ] (s, σ), [ √x ] (sx)</span></p><p><span style="font-family: arial; font-size: medium;">sy: [ right shift ] [ 1/x ] (s, σ), [ LN ] (sy)</span></p><p><span style="font-family: arial; font-size: medium;">Σx^2: [ right shift ] [ Σ+ ] (SUMS) [ e^x ] (x)</span></p><p><span style="font-family: arial; font-size: medium;">n: [ right shift ] [ Σ+ ] (SUMS) [ √x ] (n)</span></p><p><span style="font-family: arial; font-size: medium;">x-bar: [ right shift ] [ y^x ] (x-bar,y-bar) [ √x ] (x-bar)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Data: (x, y)</span></p><p><span style="font-family: arial; font-size: medium;">(10.4, 20)</span></p><p><span style="font-family: arial; font-size: medium;">(13.5, 18)</span></p><p><span style="font-family: arial; font-size: medium;">(16.8, 15)</span></p><p><span style="font-family: arial; font-size: medium;">(19.1, 13.9)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Enter statistical data: y [ENTER] x [ Σ+ ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Some stats:</span></p><p><span style="font-family: arial; font-size: medium;">x-bar = 14.95</span></p><p><span style="font-family: arial; font-size: medium;">y-bar = 16.725</span></p><p><span style="font-family: arial; font-size: medium;">r = -9.9503133E-1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Covariance: Solve for C</span></p><p><span style="font-family: arial; font-size: medium;">C = -10.555</span></p><p><span style="font-family: arial; font-size: medium;">Result is stored in C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Root Mean Square: Solve for R</span></p><p><span style="font-family: arial; font-size: medium;">R = 15.3089842903</span></p><p><span style="font-family: arial; font-size: medium;">Result is stored in R</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Z-Score Based on X Variable Statistics: Solve for Z</span></p><p><span style="font-family: arial; font-size: medium;">X? 15, Z = 1.31382E-2</span></p><p><span style="font-family: arial; font-size: medium;">X? 17, Z = 5.38666E-1</span></p><p><span style="font-family: arial; font-size: medium;">Result is stored in Z</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Formulas vs. Programs</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If we are going to evaluate formulas (that is, solve for the variable left of the equals sign), we could also enter and use programs. The programs for the above three formulas:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Covariance:</span></p><p><span style="font-family: courier; font-size: medium;">C01 LBL C</span></p><p><span style="font-family: courier; font-size: medium;">C02 r</span></p><p><span style="font-family: courier; font-size: medium;">C03 sx</span></p><p><span style="font-family: courier; font-size: medium;">C04 ×</span></p><p><span style="font-family: courier; font-size: medium;">C05 sy</span></p><p><span style="font-family: courier; font-size: medium;">C06 ×</span></p><p><span style="font-family: courier; font-size: medium;">C07 RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Root Mean Square:</span></p><p><span style="font-family: courier; font-size: medium;">R01 LBL R</span></p><p><span style="font-family: courier; font-size: medium;">R02 Σx^2</span></p><p><span style="font-family: courier; font-size: medium;">R03 n</span></p><p><span style="font-family: courier; font-size: medium;">R04 ÷</span></p><p><span style="font-family: courier; font-size: medium;">R05 SQRT</span></p><p><span style="font-family: courier; font-size: medium;">R06 RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Z Score: (x is in the X stack)</span></p><p><span style="font-family: courier; font-size: medium;">Z01 LBL Z</span></p><p><span style="font-family: courier; font-size: medium;">Z02 x-bar</span></p><p><span style="font-family: courier; font-size: medium;">Z03 -</span></p><p><span style="font-family: courier; font-size: medium;">Z04 sx</span></p><p><span style="font-family: courier; font-size: medium;">Z05 ÷</span></p><p><span style="font-family: courier; font-size: medium;">Z06 RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Byte Consumption Comparison</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Covariance</span></p><p><span style="font-family: arial; font-size: medium;">Formula: 12 bytes</span></p><p><span style="font-family: arial; font-size: medium;">Program: 10.5 bytes</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Root Mean Square</span></p><p><span style="font-family: arial; font-size: medium;">Formula: 12 bytes</span></p><p><span style="font-family: arial; font-size: medium;">Program: 9 bytes</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Z Score</span></p><p><span style="font-family: arial; font-size: medium;">Formula: 15 bytes</span></p><p><span style="font-family: arial; font-size: medium;">Program: 9 bytes</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">From sample set, programs are shorter than formulas. Is this true in general?</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-51586203029334865372023-03-25T00:00:00.000-07:002023-04-20T12:27:41.244-07:00HP 10bII+ and Sharp EL-W516T: Normal Distribution Function<p><span style="font-family: arial;"><b>HP 10bII+ and Sharp EL-W516T: Normal Distribution Function</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoSKaIxRUHUtKQN9K6LwfR_Dh4WQlu5nyhTYXgjRbwlox1GO8RQwsps8WCbB5o4Bv3AFyD7R7_FruV5BroUpLxpdkDLwgGxmuvwnVl7qpz84Lp9Ox2edmpWjT1skNsbSFF6G_W-v7jmJSwjxcMvWpbwenAcRrw4d9Ls9Ttd407bP54jW8gHZxRGoOf/s336/HP%20Prime%20-%20normal%20distribution.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="277" data-original-width="336" height="528" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoSKaIxRUHUtKQN9K6LwfR_Dh4WQlu5nyhTYXgjRbwlox1GO8RQwsps8WCbB5o4Bv3AFyD7R7_FruV5BroUpLxpdkDLwgGxmuvwnVl7qpz84Lp9Ox2edmpWjT1skNsbSFF6G_W-v7jmJSwjxcMvWpbwenAcRrw4d9Ls9Ttd407bP54jW8gHZxRGoOf/w640-h528/HP%20Prime%20-%20normal%20distribution.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Sometimes scientific calculators and financial calculators have normal distribution functions. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>HP 10bII+ Normal Distribution</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">On the HP 10bII+ financial calculator, the normal distribution functions are available at any time:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><span style="color: #2b00fe;">[ blue shift ]</span> ( z<>p ): lower tail area of normal distribution [ P(x) ]</span></p><p><span style="font-family: arial;"><span style="color: #2b00fe;">[ blue shift ]</span> ( INV) ( z<>p ): given area, get the probability</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Example:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">P(0.2) returns 0.57926</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">If the area is 0.6, z is 0.253347</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Sharp EL-W516T Normal Distribution</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The normal distribution functions offered on the Sharp EL-W516T are:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">[ MATH ] menu in SD mode:</span></p><p><span style="font-family: arial;">0) →t: convert to z</span></p><p><span style="font-family: arial;">1) P(: lower tail area</span></p><p><span style="font-family: arial;">2) Q(: I do believe it is the area between the mean and z</span></p><p><span style="font-family: arial;">3) R(: upper tail area</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The normal distribution functions are available only in the statistics mode. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Example:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">P(0.2) returns 0.57296.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Is Statistical Data Required?</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">No. In general, especially the normal distribution functions does not require or depend on any stat data. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">However, you use the stat data points to convert from x-values to convert stats to a z value in the EL-W516T using →t. Here is an example:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Data set: -3, -1, 2, 5, 6 </span></p><p><span style="font-family: arial;">Convert the data point 0 and then find the lower tail area.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">0→t= -0.524890659</span></p><p><span style="font-family: arial;">P(ANS) = 0.29983</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Eddie</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-91948476631776083342023-03-19T00:00:00.000-07:002023-04-20T12:27:41.489-07:00HP 12C: An Improved Linear Regression Function (from Curvee RPN-45 SD)<p><span style="font-family: arial; font-size: medium;"><b>HP 12C: An Improved Linear Regression Function (from Curvee RPN-45 SD)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Curvee RPN-45 Simulator</b> </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The Curvee RPN-45 from Curvee Software is an excellent app. The RPN-45 SD app is the Super-45. The Super-45 is a emulator of the classic HP 45 calculator from 1973 with the following enhancements:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The gold shift key becomes a double-shift key (<span style="color: #e69138;">gold</span>/<span style="color: #a64d79;">purple</span>)</span></p><p><span style="font-family: arial; font-size: medium;">* Complex Numbers</span></p><p><span style="font-family: arial; font-size: medium;">* 10 additional registers</span></p><p><span style="font-family: arial; font-size: medium;">* Days between dates</span></p><p><span style="font-family: arial; font-size: medium;">* Four solvers: 2 x 2 system of linear equations, 3 x 3 system of linear equations, quadratic equation, cubic equation</span></p><p><span style="font-family: arial; font-size: medium;">* Expanded statistics including full linear regression analysis</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I have purchased one on my iPod Touch (that is an iPhone without the "phone" part) for $1.99 (prices may vary). There are versions for the iPhone and iPad. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For more information: <a href="http://cuveesoft.ch/rpn45/en/index.html" target="_blank">http://cuveesoft.ch/rpn45/en/index.html</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The enhanced linear regression (L.R.) function on the Super-45 returns the following calculations to the four-level stack:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">T: covariance</span></p><p><span style="font-family: arial; font-size: medium;">Z: correlation</span></p><p><span style="font-family: arial; font-size: medium;">Y: slope</span></p><p><span style="font-family: arial; font-size: medium;">X: intercept</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The relationship between correlation (r) and covariance (cov):</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">cov(x,y) = r * sx * sy</span></p><p><span style="font-family: arial; font-size: medium;">sx = standard deviation of x-data</span></p><p><span style="font-family: arial; font-size: medium;">sy = standard deviation of y-data</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The HP 12C mimics the enhanced L.R. function. Yes, check out this app!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>HP 12C Program: Enhanced Linear Regression</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The results are stored in the following registers:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">R7 = intercept</span></p><p><span style="font-family: arial; font-size: medium;">R8 = Slope</span></p><p><span style="font-family: arial; font-size: medium;">R9 = correlation</span></p><p><span style="font-family: arial; font-size: medium;">R.0 = covariance</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In addition, I added code to calculate population deviation: σx in the x-stack, σy in the y-stack.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Step #: Code [ key ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">// linear regression function </span></p><p><span style="font-family: courier; font-size: medium;">01: 1 [ 1 ]</span></p><p><span style="font-family: courier; font-size: medium;">02: 43, 1 [ x^,r ]</span></p><p><span style="font-family: courier; font-size: medium;">03: 34 [ x<>y ]</span></p><p><span style="font-family: courier; font-size: medium;">04: 44, 9 [ STO 9 ]</span></p><p><span style="font-family: courier; font-size: medium;">05: 43, 48 [ s ]</span></p><p><span style="font-family: courier; font-size: medium;">06: 20 [ × ]</span></p><p><span style="font-family: courier; font-size: medium;">07: 20 [ × ]</span></p><p><span style="font-family: courier; font-size: medium;">08: 44, 48, 0 [ STO . 0 (decimal point, zero) ]</span></p><p><span style="font-family: courier; font-size: medium;">09: 0 [ 0 ]</span></p><p><span style="font-family: courier; font-size: medium;">10: 43, 2 [ y^, r ]</span></p><p><span style="font-family: courier; font-size: medium;">11: 44, 7 [ STO 7 ]</span></p><p><span style="font-family: courier; font-size: medium;">12: 1 [ 1 ]</span></p><p><span style="font-family: courier; font-size: medium;">13: 43, 2 [ y^, r ]</span></p><p><span style="font-family: courier; font-size: medium;">14: 34 [ x<>y ]</span></p><p><span style="font-family: courier; font-size: medium;">15: 33 [ R↓ ]</span></p><p><span style="font-family: courier; font-size: medium;">16: 34 [ x<>y ]</span></p><p><span style="font-family: courier; font-size: medium;">17: 30 [ - ]</span></p><p><span style="font-family: courier; font-size: medium;">18: 44, 8 [ STO 8 ]</span></p><p><span style="font-family: courier; font-size: medium;">19: 45, 48, 0 [ RCL . 0 (decimal point, zero) ]</span></p><p><span style="font-family: courier; font-size: medium;">20: 45, 9 [ RCL 9 ]</span></p><p><span style="font-family: courier; font-size: medium;">21: 45, 8 [ RCL 8 ]</span></p><p><span style="font-family: courier; font-size: medium;">22: 45, 7 [ RCL 7 ]</span></p><p><span style="font-family: courier; font-size: medium;">23: 43, 33, 00 [ GTO 00 ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">// population deviation</span></p><p><span style="font-family: courier; font-size: medium;">24: 45, 1 [ RCL 1 ]</span></p><p><span style="font-family: courier; font-size: medium;">25: 36 [ ENTER ]</span></p><p><span style="font-family: courier; font-size: medium;">26: 36 [ ENTER ]</span></p><p><span style="font-family: courier; font-size: medium;">27: 1 [ 1 ]</span></p><p><span style="font-family: courier; font-size: medium;">28: 30 [ - ]</span></p><p><span style="font-family: courier; font-size: medium;">29: 10 [ ÷ ]</span></p><p><span style="font-family: courier; font-size: medium;">30: 43, 21 [ √ ]</span></p><p><span style="font-family: courier; font-size: medium;">31: 44, 0 [ STO 0 ]</span></p><p><span style="font-family: courier; font-size: medium;">32: 43, 48 [ s ]</span></p><p><span style="font-family: courier; font-size: medium;">33: 45, 0 [ RCL 0 ]</span></p><p><span style="font-family: courier; font-size: medium;">34: 10 [ ÷ ]</span></p><p><span style="font-family: courier; font-size: medium;">35: 34 [ x<>y ]</span></p><p><span style="font-family: courier; font-size: medium;">36: 45, 0 [ RCL 0 ]</span></p><p><span style="font-family: courier; font-size: medium;">37: 10 [ ÷ ]</span></p><p><span style="font-family: courier; font-size: medium;">38: 34 [ x<>y ]</span></p><p><span style="font-family: courier; font-size: medium;">39: 43, 33, 00 [ GTO 00 ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Example</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Fix 6 mode is set. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Data:</span></p><p><span style="font-family: arial; font-size: medium;">(5.35, 10)</span></p><p><span style="font-family: arial; font-size: medium;">(5,70, 11)</span></p><p><span style="font-family: arial; font-size: medium;">(6.18, 12)</span></p><p><span style="font-family: arial; font-size: medium;">(6.55, 13)</span></p><p><span style="font-family: arial; font-size: medium;">(6.97, 14)</span></p><p><span style="font-family: arial; font-size: medium;">(7.36, 15)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">After entering the data points:</span></p><p><span style="font-family: arial; font-size: medium;">[ f ] (PRGM) [ R/S ]</span></p><p><span style="font-family: arial; font-size: medium;">-3.162788 (intercept), [ R↓ ]</span></p><p><span style="font-family: arial; font-size: medium;">2.465287 (slope), [ R↓ ]</span></p><p><span style="font-family: arial; font-size: medium;">0.999396 (correlation, r), [ R↓ ]</span></p><p><span style="font-family: arial; font-size: medium;">1.418000 (covariance) ( [ R↓ ] to return the stack to it's original configuration )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ g ] (GTO) 24 [ R/S ]</span></p><p><span style="font-family: arial; font-size: medium;">0.692331 ( σx ) [ x<>y ]</span></p><p><span style="font-family: arial; font-size: medium;">1.707825 ( σy )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-26799963650337928872023-03-18T00:00:00.000-07:002023-04-20T12:27:41.733-07:00TI-84 Plus CE: Tracing Polar Equations<p><span style="font-family: arial; font-size: medium;"><b>TI-84 Plus CE: Tracing Polar Equations</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b><span style="color: #2b00fe;">Traveling </span><span style="color: #38761d;">Around </span><span style="color: #e69138;">the </span>Graphs</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The programing BLINKING animates a dot around one of four polar equations:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. Ellipse</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r = b / √(1 - ε^2 * cos^2 θ), where ε = √(a^2 - b^2)/a, a > b</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. Cardioid</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r = a + (1 + cos θ)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. 3-Leaf Rose</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r = a * cos(3 * θ)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">4. Log Spiral</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r = a * e^(b * θ)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Notes:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The point alternates through blue (TI-84 Plus CE color 10), green (14), orange (15), and black (12). The graph itself is light gray (21). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r1 is the polar equation r1(θ).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Plotting points (not the polar graph) must be in cartesian coordinates (x,y). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b><span style="color: #2b00fe;">TI-84 </span><span style="color: #38761d;">Plus </span><span style="color: #e69138;">CE </span>Program: BLINKING</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">"2023-01-15 EWS"</span></p><p><span style="font-family: courier; font-size: medium;">Radian: Polar: FnOff</span></p><p><span style="font-family: courier; font-size: medium;">ZStandard</span></p><p><span style="font-family: courier; font-size: medium;">{10,14,15,12}→L6</span></p><p><span style="font-family: courier; font-size: medium;">Menu("PLOT","ELLIPSE",10,"CARDIOID",11,"3-LEAF ROSE",12,"LOG SPIRAL",13)</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 10</span></p><p><span style="font-family: courier; font-size: medium;">Disp "A≥B"</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A, B</span></p><p><span style="font-family: courier; font-size: medium;">√(A^2-B^2)/A→E</span></p><p><span style="font-family: courier; font-size: medium;">"B/√(1-E^2*cos(θ)^2)"→r1</span></p><p><span style="font-family: courier; font-size: medium;">Goto 20</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 11</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A</span></p><p><span style="font-family: courier; font-size: medium;">"A*(1+cos(θ))"→r1</span></p><p><span style="font-family: courier; font-size: medium;">Goto 20</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 12</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A</span></p><p><span style="font-family: courier; font-size: medium;">"A*cos(3*θ)"→r1</span></p><p><span style="font-family: courier; font-size: medium;">Goto 20</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 13</span></p><p><span style="font-family: courier; font-size: medium;">Disp "A>0, B>0"</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A,B</span></p><p><span style="font-family: courier; font-size: medium;">"A*e^(B*θ)"→r1</span></p><p><span style="font-family: courier; font-size: medium;">Goto 20</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 20</span></p><p><span style="font-family: courier; font-size: medium;">Input "MAX? ",M</span></p><p><span style="font-family: courier; font-size: medium;">Input "NO. STEPS? ",S</span></p><p><span style="font-family: courier; font-size: medium;">M/S→N</span></p><p><span style="font-family: courier; font-size: medium;">FnOn 1</span></p><p><span style="font-family: courier; font-size: medium;">GraphColor(1,21)</span></p><p><span style="font-family: courier; font-size: medium;">0→P: r1(P)→Q</span></p><p><span style="font-family: courier; font-size: medium;">P>Rx(Q,P)→F: P>Ry(Q,P)→G</span></p><p><span style="font-family: courier; font-size: medium;">Pt-On(F,G,1,12)</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">For(K,1,S)</span></p><p><span style="font-family: courier; font-size: medium;">Wait 0.25</span></p><p><span style="font-family: courier; font-size: medium;">Pt-On(F,G,1,21)</span></p><p><span style="font-family: courier; font-size: medium;">remainder(K,4)+1→C</span></p><p><span style="font-family: courier; font-size: medium;">K*N→P: r1(P)→Q</span></p><p><span style="font-family: courier; font-size: medium;">P>Rx(Q,P)→F: P>Ry(Q,P)→G</span></p><p><span style="font-family: courier; font-size: medium;">Pt-On(F,G,1,L6(C))</span></p><p><span style="font-family: courier; font-size: medium;">End </span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Disp "END"</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In all examples, a = 3, b = 2, maximum = 4 * π, steps = 24</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Ellipse</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr5-frp9_xMA4Q7Pn-IuNa45-odS_hwJxdL7FAOToIrG1zBPKtFspv4KgRVs9beH8bLk_44-4wYZb68FCsy6aC9uOSEwFyEvFIm8USjygGuZdMB1MzxhwsPuBuwhFPbdJ1w-QuQeKeXTpmUfU9Q0_ilHKqZMFWNYoAhkDcdfqW2b4NGa364HJEtEWC/s324/example%201%20-%20tracing%20an%20ellipse.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="244" data-original-width="324" height="482" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr5-frp9_xMA4Q7Pn-IuNa45-odS_hwJxdL7FAOToIrG1zBPKtFspv4KgRVs9beH8bLk_44-4wYZb68FCsy6aC9uOSEwFyEvFIm8USjygGuZdMB1MzxhwsPuBuwhFPbdJ1w-QuQeKeXTpmUfU9Q0_ilHKqZMFWNYoAhkDcdfqW2b4NGa364HJEtEWC/w640-h482/example%201%20-%20tracing%20an%20ellipse.png" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Cardioid</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3XSAYI-gupWkdjbfYmfj_Gp_VeHcKTqVpEgd5s1rsyrsNlRIumUBcAu7c-uwfsd48nrgfO1mkoioPgcVM0gFuUHDPMSyZ9-CHGIvHRYN5bxicNCUgUi_LVyJu8PKzxEGpjqE4HswIy86XWqKbdT6e34QEd0pTJ6zUjCjT3ah4vUflUgYmylUugWCx/s324/example%202%20-%20tracing%20a%20cardiod.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="244" data-original-width="324" height="482" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3XSAYI-gupWkdjbfYmfj_Gp_VeHcKTqVpEgd5s1rsyrsNlRIumUBcAu7c-uwfsd48nrgfO1mkoioPgcVM0gFuUHDPMSyZ9-CHGIvHRYN5bxicNCUgUi_LVyJu8PKzxEGpjqE4HswIy86XWqKbdT6e34QEd0pTJ6zUjCjT3ah4vUflUgYmylUugWCx/w640-h482/example%202%20-%20tracing%20a%20cardiod.png" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"> </span></p><p><span style="font-family: arial; font-size: medium;">3-Leaf Rose</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuKEqu_dYN1VglStSSS9DWk6ppIQoL0ud0oFDgguzClJe9dbNxcPxzIm0SpeECitT1WUV2I-M9WPMGFOjRNA23H9pYMjO1VrO_FHupZKV4ra0tp6sGYul71g1WtSdiLCSJomfmL-JzXVLSk_6J0zMorarjAei6gERpbARDKbmjHYhA4X4BLo0C5lP_/s324/example%203%20-%20tracing%20a%203-leaf%20rose.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="244" data-original-width="324" height="482" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuKEqu_dYN1VglStSSS9DWk6ppIQoL0ud0oFDgguzClJe9dbNxcPxzIm0SpeECitT1WUV2I-M9WPMGFOjRNA23H9pYMjO1VrO_FHupZKV4ra0tp6sGYul71g1WtSdiLCSJomfmL-JzXVLSk_6J0zMorarjAei6gERpbARDKbmjHYhA4X4BLo0C5lP_/w640-h482/example%203%20-%20tracing%20a%203-leaf%20rose.png" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Log Spiral</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiot50Y_uGBZFQEaKgw6pc39dhFQpAsKSC2p8M0V_Y5TIs-FEwR-rFE_fjJipIYTlVB0E20Abl11o8fouWWE_buBrMSyYUDABRJRH1WduyLqCR_i6w_gPrZqjY5H5QpDd34damOA_QCt0p-03Y3Vq9sQmJo1f8vw4ZepllluSq8TF2v7Ef8a2CHUWpk/s324/example%204%20-%20tracing%20a%20log%20spiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="244" data-original-width="324" height="482" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiot50Y_uGBZFQEaKgw6pc39dhFQpAsKSC2p8M0V_Y5TIs-FEwR-rFE_fjJipIYTlVB0E20Abl11o8fouWWE_buBrMSyYUDABRJRH1WduyLqCR_i6w_gPrZqjY5H5QpDd34damOA_QCt0p-03Y3Vq9sQmJo1f8vw4ZepllluSq8TF2v7Ef8a2CHUWpk/w640-h482/example%204%20-%20tracing%20a%20log%20spiral.png" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Source</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Harris, John W. and Horst Stocker. <u>Handbook of Mathematics and Computational Science</u> Springer: New York. 2006. ISBN 0-387-94746-9</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-45346725816216196142023-03-14T00:00:00.000-07:002023-04-20T12:27:42.223-07:00 Casio Classpad (fx-CP400): Collection of Functions<p><span style="font-family: arial; font-size: medium;">Casio Classpad (fx-CP400): Collection of Functions</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For my birthday post, on <span style="color: #2b00fe;"><b>Pi (π) Day (March 14</b></span>), here is a collection of functions for the Casio Classpad (300, 330, fx-CP400, fx-CP500). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Birthday Probability Function: bday(c,n)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"The probability that a number in a room do not share a same birthday"</span></p><p><span style="font-family: arial; font-size: medium;">c: number of categories (i.e. days in a year)</span></p><p><span style="font-family: arial; font-size: medium;">n: population size</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">bday(365, 40): 0.1087681902</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Percent Change: pchg(old, new)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">old: old amount</span></p><p><span style="font-family: arial; font-size: medium;">new: new amount</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">pchg(400,500): 25</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Combination with Repetition: nHr(n,r)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">n: population</span></p><p><span style="font-family: arial; font-size: medium;">r: number of objects to pick</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">nHr(52,5): 3819816</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Error Function and Error Compliment Function</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Error Function: erf(x)</span></p><p><span style="font-family: arial; font-size: medium;">Error Compliment Function: erfc(x)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Note that erf(x) + erfc(x) = 1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">erf(0.60): 0.6038560908</span></p><p><span style="font-family: arial; font-size: medium;">erfc(0.60): 0.3961439092</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Law of Cosines</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">a^2 = b^2 + c^2 - 2*b*c*cos(α)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Finding the Angle α: cosang(a,b,c)</span></p><p><span style="font-family: arial; font-size: medium;">Finding the Side a: cosside(b,c,α)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">(Degrees Mode)</span></p><p><span style="font-family: arial; font-size: medium;">a = 20.1, b = 18.5, c = 22.3: cosang(20.1,18.5,22.3): 58.13961834° (approx)</span></p><p><span style="font-family: arial; font-size: medium;">b = 24.2, c = 18.9, α = 58°: cosside(24.2,18.9,58): 21.4032954 (approx)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Fresnel Integrals</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Fresnel Cosine Integral: frescos(u)</span></p><p><span style="font-family: arial; font-size: medium;">C(u) = ∫( cos(π * x^2 ÷ 2) dx, 0, u)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Fresnel Sine Integral: fressin(u)</span></p><p><span style="font-family: arial; font-size: medium;">S(u) = ∫( sin(π * x^2 ÷ 2) dx, 0, u)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">frescos(1.5): 0.445261176</span></p><p><span style="font-family: arial; font-size: medium;">fressin(1.5): 0.6975049601</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Bessel Integral of the First Kind: bessel(n,x)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">J_n(x) = 1 / π * ∫( cos(n * t - x * sin t) dt, 0, π)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">bessel(0,1.5): 0.5118276716</span></p><p><span style="font-family: arial; font-size: medium;">bessel(2,1.2): 0.1593490183</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Elliptic Integral of the First Kind: ellip(x)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">K(x) = ∫( 1/ √(1 - x^2 * sin^2 t) dt, 0, π/2)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">ellip(-0.6): 1.750753803</span></p><p><span style="font-family: arial; font-size: medium;">ellip(0.4): 1.639999866</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Sine Integral: Si(x)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Si(x) = ∫( sin t / t dt, 0, x)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">Si(1.8): 1.50581678</span></p><p><span style="font-family: arial; font-size: medium;">Si(6): 1.424687551</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Beta Function: beta(a,b)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">β(a, b) = (Γ(a) * Γ(b)) ÷ Γ(a+b)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">beta(2,3): 1/12</span></p><p><span style="font-family: arial; font-size: medium;">beta(1.9,4.6): 0.04470413922 (approx)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Relativity Factor: relat(v)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">factor = √(1 - v^2/c^2)</span></p><p><span style="font-family: arial; font-size: medium;">c = 299792458 m/s</span></p><p><span style="font-family: arial; font-size: medium;">v = velocity</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">relat(201E6): 0.7419422153 (approx)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Schwarzschild Radius: schwarz(m)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">r = (2 * G * m)/c^2</span></p><p><span style="font-family: arial; font-size: medium;">G = 6.674E-11 m^3/(kg s^2)</span></p><p><span style="font-family: arial; font-size: medium;">c = 299792458 m/s</span></p><p><span style="font-family: arial; font-size: medium;">m = mass the black hole, kg</span></p><p><span style="font-family: arial; font-size: medium;">r = Schwarzschild Radius, m (event horizon)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">schwarz(7.89E30): 11717.95418</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Distance of a Drop: dropdist(v0,t)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">v0: initial velocity, m/s</span></p><p><span style="font-family: arial; font-size: medium;">t: time, s</span></p><p><span style="font-family: arial; font-size: medium;">Calculated: distance, m</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">dropdist(15,5): 197.583125</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Cycle of a Simple Pendulum: pendu(l)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l: length of a string, m</span></p><p><span style="font-family: arial; font-size: medium;">Calulated: time of the pendulum swing, s</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example: </span></p><p><span style="font-family: arial; font-size: medium;">pendu(5.5): 4.705446883</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Impedance in LRC Series Circuit: lrcser(R,f,L,C)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">R: resistance, Ω</span></p><p><span style="font-family: arial; font-size: medium;">f: frequency, Hz</span></p><p><span style="font-family: arial; font-size: medium;">L: inductance, H</span></p><p><span style="font-family: arial; font-size: medium;">C: capacity, F</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">lrcser(4,80,0.1,50E-6): 11.21437564</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Impedance in LRC Parallel Circuit: lrcpar(R,f,L,C)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">R: resistance, Ω</span></p><p><span style="font-family: arial; font-size: medium;">f: frequency, Hz</span></p><p><span style="font-family: arial; font-size: medium;">L: inductance, H</span></p><p><span style="font-family: arial; font-size: medium;">C: capacity, F</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;">lrcpar(4,80,0.1,50E-6): 3.999122191</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Source for:</b></span></p><p><span style="font-family: arial; font-size: medium;">Distance of a Drop</span></p><p><span style="font-family: arial; font-size: medium;">Cycle of a Simple Pendulum</span></p><p><span style="font-family: arial; font-size: medium;">Impedance in LRC Series Circuit</span></p><p><span style="font-family: arial; font-size: medium;">Impedance in LRC Parallel Circuit</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><u>Scientific Calculator 128 fx-1000F/fx-5000F Owner's Manual</u>. Casio. Tokyo, Japan. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Download the file here: <a href="https://drive.google.com/file/d/1M54HlJ9dP95VBEmGzkUozGzJxKGpiHMh/view?usp=share_link" target="_blank">https://drive.google.com/file/d/1M54HlJ9dP95VBEmGzkUozGzJxKGpiHMh/view?usp=share_link</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-24326390485079014572023-03-13T00:00:00.000-07:002023-04-20T12:27:42.467-07:00Review: TI-83 Premium CE Python Edition<p><span style="font-family: arial; font-size: medium;"><b>Review: TI-83 Premium CE Python Edition</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0x_AqtykzuuuO7ElLjkHU_bwTBdondLjfyiUHwiBrmSgOE7iwDgJRFDJNyB833NwTkk_8DEj2Sw4MOuEn4LGBdKl1Hazntx61K5cZWEaam7TozayRSy9b6GaW_Q--MnJaxVOEPQtnGUwUu5ent_w0EvAwSjasNHGebQ8kP36ZVjrLKlUipRtvBaNE/s3828/ti83pce%20full.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3828" data-original-width="1619" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0x_AqtykzuuuO7ElLjkHU_bwTBdondLjfyiUHwiBrmSgOE7iwDgJRFDJNyB833NwTkk_8DEj2Sw4MOuEn4LGBdKl1Hazntx61K5cZWEaam7TozayRSy9b6GaW_Q--MnJaxVOEPQtnGUwUu5ent_w0EvAwSjasNHGebQ8kP36ZVjrLKlUipRtvBaNE/w270-h640/ti83pce%20full.jpg" width="270" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Quick Facts</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Model: TI-83 Premium CE Python Edition</span></p><p><span style="font-family: arial; font-size: medium;">Company: Texas Instruments</span></p><p><span style="font-family: arial; font-size: medium;">Price: $90 - $130 US Dollars </span></p><p><span style="font-family: arial; font-size: medium;">Country of Origin: France</span></p><p><span style="font-family: arial; font-size: medium;">Power: Rechargeable</span></p><p><span style="font-family: arial; font-size: medium;">USB Cord: Standard A to Mini-B</span></p><p><span style="font-family: arial; font-size: medium;">Memory: 154,000 bytes RAM, 3MB ROM</span></p><p><span style="font-family: arial; font-size: medium;">Display size: color, backlit, 240 x 320 pixels</span></p><p><span style="font-family: arial; font-size: medium;">Operating System: Algebraic</span></p><p><span style="font-family: arial; font-size: medium;">Are programs compatible with TI-84 Plus CE? Yes, both TI-BASIC and Python programs through TI Connect CE.</span></p><p><span style="font-family: arial; font-size: large;">Essentially the TI-83 Premium</span><span style="font-family: arial; font-size: large;"> CE Python Edition and TI-84 Plus CE Python (of the United States) are similar. The French TI-83 Premium CE Python was first released in 2019, two years prior to the TI-84 Plus CE Python. </span></p><p><i style="font-family: arial; font-size: large;">I note at this time, March 2023, finding TI-84 Plus CE Python calculators to buy are extremely hard to find due to global chip shortage.</i><span style="font-family: arial; font-size: large;"> </span></p><p><span style="font-family: arial; font-size: medium;">The TI-83 </span><span style="font-family: arial; font-size: large;">Premium</span><span style="font-family: arial; font-size: large;"> </span><span style="font-family: arial; font-size: medium;">CE Python Edition is based off of the TI-83 </span><span style="font-family: arial; font-size: large;">Premium</span><span style="font-family: arial; font-size: large;"> </span><span style="font-family: arial; font-size: medium;">CE but it has an additional ARM chip that gives the calculator the Python, specifically CircuitPython. We have a similar structure for the TI-84 Plus CE Python. </span></p><p><span style="font-family: arial; font-size: large;">My review on the American TI-84 Plus CE Python: </span><a href="http://edspi31415.blogspot.com/2021/07/review-ti-84-plus-ce-python.htm" style="font-family: arial; font-size: large;" target="_blank">http://edspi31415.blogspot.com/2021/07/review-ti-84-plus-ce-python.htm</a><span style="font-family: arial; font-size: large;">l</span></p><p><span style="font-family: arial; font-size: large;">The rest of the blog is going to highlight some comparisons</span><span style="font-family: arial; font-size: large;"> and unique features.</span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><b>QPiRac: The Exact Calculator Engine</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieCKLVOmKkeAvBxuNoclTtIdgjmvIZWy8xTThi15SOPWelvgQz52kejuCeOudcrGgBamlRE5Rfgm4xI7FpKsI7irzulg_BuWUMBGRaCsFjByO2_PJqz7kqg3Q81hWo_OafyeLwDOGl4wuG9YR25SnhhCfNp292q-dnO1rVM4GCVYqJ0W1uhoodD95r/s770/exact%20engine%20comparison.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="584" data-original-width="770" height="486" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieCKLVOmKkeAvBxuNoclTtIdgjmvIZWy8xTThi15SOPWelvgQz52kejuCeOudcrGgBamlRE5Rfgm4xI7FpKsI7irzulg_BuWUMBGRaCsFjByO2_PJqz7kqg3Q81hWo_OafyeLwDOGl4wuG9YR25SnhhCfNp292q-dnO1rVM4GCVYqJ0W1uhoodD95r/w640-h486/exact%20engine%20comparison.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZkIRwt8IvqIeq75GRbz86E5JFKo1EElZpPuybqGL2nShr6y0DYFf0lDJ1xxK6H1qrF_ShvMFTbbaaeV4BX69I75kY_MbQDNz1fwKoLWPtmkppmUFP0v-RiBLRCHR0Rw7vZzeA-RpmWLFb4xohv8P1jyxyOidynk4sNOP5i4BLSi6NwmuZ21aG7G_H/s1104/program%20exact%20math%20comparison.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="349" data-original-width="1104" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZkIRwt8IvqIeq75GRbz86E5JFKo1EElZpPuybqGL2nShr6y0DYFf0lDJ1xxK6H1qrF_ShvMFTbbaaeV4BX69I75kY_MbQDNz1fwKoLWPtmkppmUFP0v-RiBLRCHR0Rw7vZzeA-RpmWLFb4xohv8P1jyxyOidynk4sNOP5i4BLSi6NwmuZ21aG7G_H/w640-h202/program%20exact%20math%20comparison.jpg" width="640" /></a></div><br /><p><span style="font-family: arial; font-size: large;">I wish the TI-84 Plus CE had this: exact calculations, which is known as QPiRac. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Q: fractions</span></p><p><span style="font-family: arial; font-size: medium;">Pi: terms of π</span></p><p><span style="font-family: arial; font-size: medium;">Rac: radicals (square roots)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The TI-36X Pro (and TI-30X Pro MathPrint) also has exact math. We can convert between approximate and exact answers by pressing the [ <> ] button. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Keyboard Differences</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">TI-83 Premium CE Python keypad:</span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj66js8Ecd2R3zFJtmYPu0yqOBEQeuupaGTfyKX6sMWFMsgR6-kDstSS7BE0fOGIPWTCE_-5aqTdTWpqOM0MTn76l37k_gxjSqj48b1fwKWi3jz0HXxOsf482FOXSUZU1x0j08eLaatwYNVOXgdvLcGH9QyAtP1A8WRlqwjMYz8zIoymFRYmE1Hi5eS/s4624/TI-83PCE%20closeup.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3468" data-original-width="4624" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj66js8Ecd2R3zFJtmYPu0yqOBEQeuupaGTfyKX6sMWFMsgR6-kDstSS7BE0fOGIPWTCE_-5aqTdTWpqOM0MTn76l37k_gxjSqj48b1fwKWi3jz0HXxOsf482FOXSUZU1x0j08eLaatwYNVOXgdvLcGH9QyAtP1A8WRlqwjMYz8zIoymFRYmE1Hi5eS/w640-h480/TI-83PCE%20closeup.jpg" width="640" /></a></div><div><br /></div><div><br /></div><div><span style="font-family: arial; font-size: medium;">TI-84 Plus CE Python keypad:</span></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5VN0L0vrhnBxAsdfc_J5FJtrcMpEzsU54OrKT1Mt5NAQSpezZx5gYtCW1rk2Jm-yf_-HSfEPYuEi2cFeMkVcJw4--N9UA4H9ebuaBWyFekZCnP_gv7CL-1-ek6GjJec20FYNqIvHEg-YWlXnQDqSleqVKRq5Km24kEVGVT1l6BtBGIu11LZDrwm4G/s4624/TI-84PCE%20closeup.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3468" data-original-width="4624" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5VN0L0vrhnBxAsdfc_J5FJtrcMpEzsU54OrKT1Mt5NAQSpezZx5gYtCW1rk2Jm-yf_-HSfEPYuEi2cFeMkVcJw4--N9UA4H9ebuaBWyFekZCnP_gv7CL-1-ek6GjJec20FYNqIvHEg-YWlXnQDqSleqVKRq5Km24kEVGVT1l6BtBGIu11LZDrwm4G/w640-h480/TI-84PCE%20closeup.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A lot of the keys between the TI-83 Premium CE and the TI-84 Plus CE (and their respective Python editions) differ even though the features between the two calculators are pretty much the same. Keep in mind the keys on the TI-83 Premium CE are in French, while the keys on the TI-84 Plus CE are in English. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The fraction shortcut template is a shortcut is accessed on the TI-84 Plus CE by the key sequence [ alpha ] [ X,T,θ,n ]. On the TI-83 Premium CE, the fraction template is its own key.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The reciprocal function is a primary key on the TI-84 Plus CE, but it is a secondary function of the matrix key, [ matrice ], on the TI-83 Premium CE.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* Speaking of matrices, the menu is a primary key on the TI-83 Premium CE, mainly the [ matrice ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* Instead of separate keys, all the trigonometric and inverse trigonometric functions are accessed by the [ trig ] key on the TI-83 Premium CE. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The solver and the PlySmlt2 (polynomial and simultaneous equations) are accessed by the [ résol ] key on the TI-83 Premium CE.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The TI-83 Premium CE has a template popup menu, accessed by pressing [ 2nd ] [ []/[] ] (∫ [] d []>).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The [ annul ] key on the TI-83 Premium CE is the [ clear ] key on the TI-84 Plus CE.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The [ suppr ] key on the TI-83 Premium CE is the [ del ] (delete) key on the TI-84 Plus CE.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The insérer function on the TI-83 Premium CE is the ins (insert) function on the TI-84 Plus CE.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The applications key is moved to the 2nd function on the [ résol ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The pi (π) constant is a 2nd function of the [ ^ ] key on the TI-84 Plus CE, but the 2nd function of the [ trig ] key on the TI-83 Premium CE. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* The stats menu on the TI-83 Premium CE has a Quartiles Setting, something that is not present on the TI-84 Plus CE. I did not realize that there are different methods to determine quartiles. The options presented are TI-83CE method and TI-8x method. This is something I have to read about. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha8w1IsfaOWNfyI4hEWBZ-y214ShILiqj1ln1UoBjMAszOgP_0UfT9aGCGXwr2skeUtxJGjQE-vpVrNkcJu6ET5fcin0_uBBMaJmTY79yIPdVJfpVVlAWn4d-NjAXRSjOmi26MelO1wIpWqeyDsqL2BZzWO3nIgPfQ_gZsJueSpXk1zXh2s814t6kZ/s770/TI-83PCE%20unique%20menus.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="770" height="582" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha8w1IsfaOWNfyI4hEWBZ-y214ShILiqj1ln1UoBjMAszOgP_0UfT9aGCGXwr2skeUtxJGjQE-vpVrNkcJu6ET5fcin0_uBBMaJmTY79yIPdVJfpVVlAWn4d-NjAXRSjOmi26MelO1wIpWqeyDsqL2BZzWO3nIgPfQ_gZsJueSpXk1zXh2s814t6kZ/w640-h582/TI-83PCE%20unique%20menus.jpg" width="640" /></a></div><p></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Final Thoughts</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I like the TI-83 Premium CE Python Edition, it's got the exact math engine, and it's not just limited to the Home Screen. The exact math engine extends to the all the apps except for Python. Even TI-Basics programs have the exact math engine, which is a pleasant surprise. If you are looking for a TI Python but not an Nspire, the TI-83 Premium CE Python Edition is worth checking out. </span></p><p><span style="font-family: arial; font-size: large;">Still hoping for more color options and the base conversions.</span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><b>Sources</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Shore, Edward. "Review: TI-84 Plus CE Python" Eddie's Math and Calculator Blog. July 19, 2021. <a href="http://edspi31415.blogspot.com/2021/07/review-ti-84-plus-ce-python.html" target="_blank">http://edspi31415.blogspot.com/2021/07/review-ti-84-plus-ce-python.html</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"TI-83 Premium CE" Wikipedia. Last Updated October 25, 2021. Accessed March 2, 2023. <a href="https://en.wikipedia.org/wiki/TI-83_Premium_CE" target="_blank">https://en.wikipedia.org/wiki/TI-83_Premium_CE</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Woerner, Joerg. "TI-83 Premium CE Edition Python" Datamath Calculator Museum. May 30, 2019. <a href="http://www.datamath.org/Graphing/TI-83PRCE.htm" target="_blank">http://www.datamath.org/Graphing/TI-83PRCE.htm</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-92211588621392135862023-03-12T00:00:00.000-08:002023-04-20T12:27:42.717-07:00Casio fx-CG50: Logistic Equation - Solving For Parameters From Two Data Points<p><span style="font-family: arial; font-size: medium;"><b>Casio fx-CG50: Logistic Equation - Solving For Parameters From Two Data Points</b></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The Challenge</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">It can be a challenge, especially without a statistics software package or method like the maximum likelihood estimate, to fit data (x, p), to the curve:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">p(x) = 1 / ( 1 + α * x^β ) = ( 1 + α * x^β )^-1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">What happens if we just have two data points (x1, p1) and (x2, p2). Then finding α and β turns into simpler task. Either we find a quick estimate to extend to other data points or if we just have two data points, exact solutions.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Finding α and β</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">With the points (x1, p1) and (x2, p2), the system to solve is:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1 / ( 1 + α * x1^β ) = p1</span></p><p><span style="font-family: arial; font-size: medium;">1 / ( 1 + α * x2^β ) = p2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1 + α * x1^β = 1/p1</span></p><p><span style="font-family: arial; font-size: medium;">1 + α * x2^β = 1/p2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α * x1^β = 1/p1 - 1</span></p><p><span style="font-family: arial; font-size: medium;">α * x2^β = 1/p2 - 1 </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Assuming that α ≠ 0, divide both equations to get:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x1^β / x2^β = (1/p1 - 1) / (1/p2 - 1)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Solve for β:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">(x1/x2)^β = (1/p1 - 1) / (1/p2 - 1)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">ln [ (x1/x2)^β ] = ln [ (1/p1 - 1) / (1/p2 - 1) ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">β * ln [ (x1/x2) ] = ln [ (1/p1 - 1) / (1/p2 - 1) ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">β = ln [ (1/p1 - 1) / (1/p2 - 1) ] / ln [ (x1/x2) ] </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Then we can get α: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α = (1/p1 - 1) / (x1^β) = (1/p2 - 1) / (x2^β) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Casio fx-CG50 Program: BETPARAM</b></span></p><p><span style="font-family: arial; font-size: medium;">(276 bytes)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The characters α and β are found in the CHAR sub menu (outside of the PRGM menu). If you have a monochrome calculator or just don't want color, ignore the color commands.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program then graphs the resulting equation. The variables Y1 and Y2 (with the bold Y) represent functions of X. </span></p><p><span style="font-family: arial; font-size: medium;"> </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;"><b>Red "P(X)=1÷(1+αX^β)"</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"SOLVE FOR α, β"◢</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Rad</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"POINT 1"</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"X1"?→Y</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"P1"?→Q</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"POINT 2"</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"X2"?→Z</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"Y2"?→R</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>ln ((Q^-1 -1)÷(R^1 - 1))</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Ans÷ln (Y÷Z)→B</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>(Q^-1 - 1)÷(Y^B)→A</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>ClrText</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Blue Locate 1,3,"EST. PARAMETERS"</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Locate 1,4,"α="</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Locate 5,4,A</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Locate 1,5,"β="</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>Locate 5,5,B</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>"1÷(1+A×X^B)"→Y1</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>""→Y2</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>SetG-Color Green,1</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>DrawGraph</b></span></p><p><span style="font-family: courier; font-size: medium;"><b>ZoomAuto</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 1:</span></p><p><span style="font-family: arial; font-size: medium;">(x1, p1) = (0.5, 0.76)</span></p><p><span style="font-family: arial; font-size: medium;">(x2, p2) = (1.5, 0.70)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjsT-F8Y_N1ziWTr9aaJmRBv41dGsYUIDQz-pW0abPJW8OS6ShRfC0uRrw6i-WKPn4dv1CLk7oA7QspBFjIqwkvNi1tKXwHfqb68w07GycK99E3Fw2Q-hO8NLi0LKv3UuHxKPoe0sfE-CFDtDq4hV9cXAfbKyo3ApuINJ3GIDLIUX9kzbtj-7VaXPi/s844/Example%201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="498" data-original-width="844" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjsT-F8Y_N1ziWTr9aaJmRBv41dGsYUIDQz-pW0abPJW8OS6ShRfC0uRrw6i-WKPn4dv1CLk7oA7QspBFjIqwkvNi1tKXwHfqb68w07GycK99E3Fw2Q-hO8NLi0LKv3UuHxKPoe0sfE-CFDtDq4hV9cXAfbKyo3ApuINJ3GIDLIUX9kzbtj-7VaXPi/w640-h378/Example%201.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 2:</span></p><p><span style="font-family: arial; font-size: medium;">(x1, p1) = (3/2, 5/8)</span></p><p><span style="font-family: arial; font-size: medium;">(x2, p2) = (2/3, 3/8)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCf8_N7sK5ps7y1jJEdc-WQDxh88YucLUmRlxMKVHSutZlvqIkJEoXMazCMnkaCGqHNTLGhZL-9WbRxexRSVf27fqtQsRxGCu7kxub0-gNIIZzAMCKQcHGjIK0GTVkhF6DbH5wRuEp0TJjcDQRBDrEbBIN6K9qSEB-0qo-KankcVKn4EApauFbLxrl/s830/Example%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="484" data-original-width="830" height="374" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCf8_N7sK5ps7y1jJEdc-WQDxh88YucLUmRlxMKVHSutZlvqIkJEoXMazCMnkaCGqHNTLGhZL-9WbRxexRSVf27fqtQsRxGCu7kxub0-gNIIZzAMCKQcHGjIK0GTVkhF6DbH5wRuEp0TJjcDQRBDrEbBIN6K9qSEB-0qo-KankcVKn4EApauFbLxrl/w640-h374/Example%202.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Source:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sumpter, David. <u>The Ten Equations That Rule the World: And How You Can use Them Too.</u> Flatiron Books: New York. 2021. ISBN 978-1-250-24696-7</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-15124847889642966922023-03-11T00:00:00.000-08:002023-04-20T12:27:42.963-07:00Casio fx-CG50: Plotting the Betting Equation<p><span style="font-family: arial; font-size: medium;"><b>Casio fx-CG50: Plotting the Betting Equation</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program BETPLOT plots two equations:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The betting equation, based on logistic equation:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y1(x) = p(x) = 1 / (1 + α*x^β)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α, β: parameters</span></p><p><span style="font-family: arial; font-size: medium;">x: data point, odds given by the booker</span></p><p><span style="font-family: arial; font-size: medium;">p(x): probability, probability that a favorite event happens/wins</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The expected profit equation:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y2(x) = p(x) * x - (1 - p(x))</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Casio fx-CG 50 Program: BETPLOT</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The characters α, β, and # are found in the CHAR sub menu (outside of the PRGM menu). If you have a monochrome calculator or just don't want color, ignore the color commands.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program then graphs the resulting equation. The variables Y1 and Y2 (with the bold Y) represent functions of X. </span></p><p><span style="font-family: arial; font-size: medium;"> </span></p><p><span style="font-family: courier; font-size: medium;">"BETTING EQN."</span></p><p><span style="font-family: courier; font-size: medium;">"DAVID SUMPTER"</span></p><p><span style="font-family: courier; font-size: medium;">Red "1÷(1+αX^β)"◢</span></p><p><span style="font-family: courier; font-size: medium;">"INCREMENT"?→1</span></p><p><span style="font-family: courier; font-size: medium;">"# STEPS"?→S</span></p><p><span style="font-family: courier; font-size: medium;">"α"?→A</span></p><p><span style="font-family: courier; font-size: medium;">"β"?→B</span></p><p><span style="font-family: courier; font-size: medium;">"(1+A×X^B)^-1"→<b>Y</b>1</span></p><p><span style="font-family: courier; font-size: medium;">"X×Y1-(1-Y1)"→<b>Y</b>2</span></p><p><span style="font-family: courier; font-size: medium;">Y=type</span></p><p><span style="font-family: courier; font-size: medium;">SetG-Color Black, 1</span></p><p><span style="font-family: courier; font-size: medium;">SetG-Color Green, 2</span></p><p><span style="font-family: courier; font-size: medium;">Seq(K,K,0,S×I+I,I)→List 1</span></p><p><span style="font-family: courier; font-size: medium;">(1+A×List 1^B)^-1→List 2</span></p><p><span style="font-family: courier; font-size: medium;">List 2×List1-(1-List 2)→List 3</span></p><p><span style="font-family: courier; font-size: medium;">ClrText</span></p><p><span style="font-family: courier; font-size: medium;">"COL. 1: X"</span></p><p><span style="font-family: courier; font-size: medium;">"COL. 2: P(X)"</span></p><p><span style="font-family: courier; font-size: medium;">"COL. 3: EXP. WIN"◢</span></p><p><span style="font-family: courier; font-size: medium;">List→Mat(List 1,List 2,List 3)◢ </span></p><p><span style="font-family: courier; font-size: medium;">ViewWindow 0,S×I,I,Min(List 2)-1,Max(List 2),0.25</span></p><p><span style="font-family: courier; font-size: medium;">AxesOn</span></p><p><span style="font-family: courier; font-size: medium;">GridOn</span></p><p><span style="font-family: courier; font-size: medium;">DrawGraph</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 1:</span></p><p><span style="font-family: arial; font-size: medium;">α = 1.3, β = 1.01</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRk9xiUDIEXGwyaHhfLCw-ND9cHm6_eV3gwrR5p89ji3jROlc5CO15EPWeqkGsl9_2WME6RKoLaDHIqJV4YUFIvsisgItSuzeR_r3iaq2G5IbtD7PkFuyfExQuIz5jKR-1bleMIbfkooHsgosW53CZRV1KqpSIC9PkGEtj25BlJ0X6NJ0UbgHUg05K/s817/bet%20plot%20example%201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="479" data-original-width="817" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRk9xiUDIEXGwyaHhfLCw-ND9cHm6_eV3gwrR5p89ji3jROlc5CO15EPWeqkGsl9_2WME6RKoLaDHIqJV4YUFIvsisgItSuzeR_r3iaq2G5IbtD7PkFuyfExQuIz5jKR-1bleMIbfkooHsgosW53CZRV1KqpSIC9PkGEtj25BlJ0X6NJ0UbgHUg05K/w640-h376/bet%20plot%20example%201.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 2:</span></p><p><span style="font-family: arial; font-size: medium;">α = 1.16, β = 1.25</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxJy1bisl05K_1c7tC7qseCSWdsUc0x5guU-tYNcxQocvFbW6E9bZsRnG_WsHO943Y1jM2wNAORqDfDa1Q3ziLu8PGBloh9geQ_d2aQvGAbvR8ad7UZBog4LVsT-syZQxWaJTGxBxV416CFAhgLYY3VpQY-UqDZ-I6pZ8-tbFb9-izqJZ63FDvHP1C/s818/bet%20plot%20example%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="479" data-original-width="818" height="374" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxJy1bisl05K_1c7tC7qseCSWdsUc0x5guU-tYNcxQocvFbW6E9bZsRnG_WsHO943Y1jM2wNAORqDfDa1Q3ziLu8PGBloh9geQ_d2aQvGAbvR8ad7UZBog4LVsT-syZQxWaJTGxBxV416CFAhgLYY3VpQY-UqDZ-I6pZ8-tbFb9-izqJZ63FDvHP1C/w640-h374/bet%20plot%20example%202.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Source:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sumpter, David. <u>The Ten Equations That Rule the World: And How You Can use Them Too</u>. Flatiron Books: New York. 2021. ISBN 978-1-250-24696-7</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-76565355254433232492023-03-05T00:00:00.000-08:002023-04-20T12:27:43.211-07:00Radio Shack EC-4000 (equiv. of TI-57): Program Library<p><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000 (equiv. of TI-57): Program Library</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX2yvSNcHSn97zmcnWvYp8_R8-_RxycQrrSK4NerN24LNmFhMOhg9rB5EaBJp5jGBr0JJdWCyWAxkHVVLnYZj6xGVlaKiPrP7HH7ELZ0wPZbrnqkBI1L3DMpVZJ3ucFurftSGSjzsQIFaZQ6RtMPxB6-M03i5QQ1fRUffBzLrhjyXoMBLZNAmdxJ9c/s4624/20230102_092712.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX2yvSNcHSn97zmcnWvYp8_R8-_RxycQrrSK4NerN24LNmFhMOhg9rB5EaBJp5jGBr0JJdWCyWAxkHVVLnYZj6xGVlaKiPrP7HH7ELZ0wPZbrnqkBI1L3DMpVZJ3ucFurftSGSjzsQIFaZQ6RtMPxB6-M03i5QQ1fRUffBzLrhjyXoMBLZNAmdxJ9c/w480-h640/20230102_092712.jpg" width="480" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000/TI-57: Horner's Method</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Let's start with a demonstration of Horner's Method, which allows a quick evaluation of polynomials. For a quadratic polynomial:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">p(x) = a * x^2 + b * x + c = x * (a * x + b) + c</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program demonstrates an example polynomial:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">p(x) = 3 * x^2 - 4 * x + 9 = x * (3 * x - 4) + 9</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Step: Key Code [ Key ]</span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>00: 32, 1 [ STO 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>01: 55 [ × ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>02: 03 [ 3 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>03: 65 [ - ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>04: 04 [ 4 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>05: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>06: 55 [ × ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>07: 33, 1 [ RCL 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>08: 75 [ + ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>09: 09 [ 9 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>10: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>11: 81 [ R/S ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>12: 71 [ RST ]</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples:</span></p><p><span style="font-family: arial; font-size: medium;">p(0) = 9</span></p><p><span style="font-family: arial; font-size: medium;">p(5) = 64</span></p><p><span style="font-family: arial; font-size: medium;">p(9) = 216</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Horner's Method can apply to higher order polynomials. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000/TI-57: Permutation and Factorial</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This is to add two of the common probability functions that are missing with on the calculator. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">nPr = n! / (n - r)!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If n = r, then nPn = n!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Store n in R0 (register 0), r in R1 (register 1), then run the program (RST, R/S).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Other registers used: R2: nPr, R7: n-r+1 </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Note that R7 is also the t-register. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Step: Key Code [ Key ]</span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>00: 01 [ 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>01: 32, 2 [ STO 2 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>02: 33, 0 [ RCL 0 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>03: 65 [ - ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>04: 33, 1 [ RCL 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>05: 75 [ + ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>06: 01 [ 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>07: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>08: 32, 7 [ STO 7 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>09: 86, 5 [ LBL 5 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>10: 33, 0 [ RCL 0 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>11: 39, 2 [ Prd 2 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>12: 01 [ 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>13: -34, 0 [ INV SUM 0 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>14: 33, 0 [ RCL 0 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>15: 76 [ x≥t ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>16: 51, 5 [ GTO 5 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>17: 33, 2 [ RCL 2 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>18: 81 [ R/S ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>19: 71 [ RST ]</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples:</span></p><p><span style="font-family: arial; font-size: medium;">n = 6, r = 6: 6P6 = 6! = 720</span></p><p><span style="font-family: arial; font-size: medium;">n = 5, r = 3: 5P3 = 60</span></p><p><span style="font-family: arial; font-size: medium;">n = 11, r = 6: 11P6 = 332,640</span></p><p><span style="font-family: arial; font-size: medium;">n = 52, r = 5: 52P5 = 3.118752 * 10^8</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000/TI-57: Snell's Law</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There are two subroutines in this program listing. Subroutines accessed by the [ SBR ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Snell's Law describes, among other things, the relationship between index of refraction of a medium (n) and refraction angle of the direction of light (Θ) is stated by:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">n1 * sin(Θ1) = n2 * sin(Θ2)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Subroutine 1: Solve for n2. n2 = (n1 * sin(Θ1)) / sin(Θ2)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Subroutine 2: Solve for Θ2. Θ2 = arcsin( n1 * sin(Θ1) / n2 )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The registers used are: R1 = n1, R2 = n2, R3 = Θ1, R4 = Θ2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Step: Key Code [ Key ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">// Solve for n2</span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>00: 86, 1 [ LBL 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>01: 50 [ DEG ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>02: 33, 1 [ RCL 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>03: 55 [ × ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>04: 33, 3 [ RCL 3 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>05: 28 [ SIN ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>06: 45 [ ÷ ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>07: 33, 4 [ RCL 4 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>08: 28 [ SIN ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>09: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>10: 32, 2 [ STO 2 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>11: 81 [ R/S ]</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">// Solve for Θ2</span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>12: 86, 2 [ LBL 2 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>13: 50 [ DEG ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>14: 33, 1 [ RCL 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>15: 55 [ × ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>16: 33, 3 [ RCL 3 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>17: 28 [ SIN ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>18: 45 [ ÷ ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>19: 33, 2 [ RCL 2 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>20: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>21: -28 [ INV SIN ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>22: 32, 4 [ STO 4 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>23: 81 [ R/S ]</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Solve for n2: n1 = 1.000293 (air), Θ1 = 30°, Θ2 = 19°</span></p><p><span style="font-family: arial; font-size: medium;">1.000293 STO 1</span></p><p><span style="font-family: arial; font-size: medium;">30 STO 3</span></p><p><span style="font-family: arial; font-size: medium;">19 STO 4</span></p><p><span style="font-family: arial; font-size: medium;">GSB 1</span></p><p><span style="font-family: arial; font-size: medium;">Result: n2: 1.5362267</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Solve for Θ2: n1 = 1.000293 (air), Θ1 = 30°, n2 = 1.333 (water)</span></p><p><span style="font-family: arial; font-size: medium;">1.000293 STO 1</span></p><p><span style="font-family: arial; font-size: medium;">30 STO 3</span></p><p><span style="font-family: arial; font-size: medium;">1.333 STO 2</span></p><p><span style="font-family: arial; font-size: medium;">GSB 2</span></p><p><span style="font-family: arial; font-size: medium;">Result: Θ2: 22.036902</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000/TI-57: Pseudorandom Number Generation</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This program attempts to generate random numbers using the generator:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x_n+1 = frac(997 * x_n + π)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The random numbers are between 0 and 1. An initial seed will be required </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The calculator does not have fraction and integer parts, so they have to be simulated:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">int(x) ≈ x + 1E10 - 1E10</span></p><p><span style="font-family: arial; font-size: medium;">frac(x) = x - int(x), will require a register </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">See steps 10 to 23. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: red; font-family: arial; font-size: medium;"><i>Due to the internal 10 digits and the simulations, expect possible roundoff errors as random numbers are continuously generated. </i></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Step: Key Code [ Key ]</span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>00: 55 [ × ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>01: 09 [ 9 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>02: 09 [ 9 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>03: 07 [ 7 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>04: 75 [ + ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>05: 30 [ π ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>06: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>07: 32, 6 [ STO 6 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>08: 75 [ + ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>09: 01 [ 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>10: 42 [ EE ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>11: 01 [ 1 ] </b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>12: 00 [ 0 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>13: 65 [ - ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>14: 01 [ 1 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>15: 42 [ EE ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>16: 01 [ 1 ] </b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>17: 00 [ 0 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>18: 85 [ = ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>19: -42 [ INV EE ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>20: -34,6 [ INV SUM 6 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>21: 33, 6 [ RCL 6 ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>22: 81 [ R/S ]</b></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>23: 71 [ RST ]</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Seed: 0.98</span></p><p><span style="font-family: arial; font-size: medium;">Generation:</span></p><p><span style="font-family: arial; font-size: medium;">0.2015927</span></p><p><span style="font-family: arial; font-size: medium;">0.1294647</span></p><p><span style="font-family: arial; font-size: medium;">0.2178986</span></p><p><span style="font-family: arial; font-size: medium;">0.3864470</span></p><p><span style="font-family: arial; font-size: medium;">0.4292517</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Until next time,</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-64954391452486035832023-03-04T00:00:00.000-08:002023-04-20T12:27:43.458-07:00 Radio Shack EC-4000 (equiv. of TI-57): Linear Regression<p><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000 (equiv. of TI-57): Linear Regression</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiml0pzq9hMnogRdnaAFqlTeO-wDHk7Lyqx58uWMoFDG3ZY6RgKs6Z6nIa1fumxl2jI0Ae--11VYls6pE7pGw7f-524yjFBxHJzsS_4ch6jI2R-SGibdxoHf-Ivj-MnQan6l9Jb52ou3TAJqpVUtQWLGHUht5wrjRdN7SqmaqTakiURSzJacJUnpXXQ/s4624/20230102_092715.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiml0pzq9hMnogRdnaAFqlTeO-wDHk7Lyqx58uWMoFDG3ZY6RgKs6Z6nIa1fumxl2jI0Ae--11VYls6pE7pGw7f-524yjFBxHJzsS_4ch6jI2R-SGibdxoHf-Ivj-MnQan6l9Jb52ou3TAJqpVUtQWLGHUht5wrjRdN7SqmaqTakiURSzJacJUnpXXQ/w480-h640/20230102_092715.jpg" width="480" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The TI-57 Clone and the Statistics</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The Radio Shack EC-4000, which is identical to the 1977 Texas Instruments TI-57 programming calculator. The calculators have a program space of 50 programming steps with a simple function set. We get loops and tests, but the statistics kind of lack. Despite this, the EC-4000 can work with two variable statistics.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Entering bivariate data: x [ x<>t ] y [ 2nd ] ( Σ+ )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2nd xbar (x with a bar over the x): mean of x data (1 variable); mean of y data (2 variable)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">INV 2nd xbar: mean of x data (2 variable)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2nd σ^2: variance of x data (1 variable), variance of y data (2 variable)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">INV 2nd σ^2: variance of x data (2 variable)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Registers:</span></p><p><span style="font-family: arial; font-size: medium;">R0 = n</span></p><p><span style="font-family: arial; font-size: medium;">R1 = Σy</span></p><p><span style="font-family: arial; font-size: medium;">R2 = Σy^2</span></p><p><span style="font-family: arial; font-size: medium;">R3 = Σx</span></p><p><span style="font-family: arial; font-size: medium;">R4 = Σx^2</span></p><p><span style="font-family: arial; font-size: medium;">R5 = Σxy</span></p><p><span style="font-family: arial; font-size: medium;">R7: use for data entry</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This leaves R6 is available for calculations. </span></p><div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><b>Formulas Used</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">y = a * x + b</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">a: slope</span></div><div><span style="font-family: arial; font-size: medium;">b: y-intercept</span></div><div><span style="font-family: arial; font-size: medium;">r^2: r-square (closer to 1 is best)</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Simplifying the formulas in order to fit the three formulas within 50 steps:</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">a = ( Σx * ybar - Σxy ) / ( xbar * Σx - Σx^2 )</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">b = ybar - a * xbar</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">r^2 = abs( a * ( Σx * ybar - Σxy) / ( Σy^2 - Σy * ybar ) )</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><b>Radio Shack EC-4000/TI-57 Program: Linear Regression</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Output: [ R/S ] a [ R/S ] b [ R/S ] r^2</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Step #: Code [ key ]</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">// Calculate a (slope):</span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>00: 43 [ ( ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>01: 33,3 [ RCL 3 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>02: 55 [ × ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>03: 89 [ xbar ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>04: 65 [ - ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>05: 33,5 [ RCL 5 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>06: 44 [ ) ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>07: 45 [ ÷ ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>08: 43 [ ( ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>09: -89 [ INV xbar ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>10: 55 [ × ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>11: 33, 3 [ RCL 3 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>12: 65 [ - ] </b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>13: 33, 4 [ RCL 4 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>14: 85 [ = ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>15: 32, 6 [ STO 6 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>16: 81 [ R/S ]</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">// Calculate b (y-intercept):</span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>17: 89 [ xbar ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>18: 65 [ - ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>19: 33, 6 [ RCL 6 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>20: 55 [ × ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>21: -89 [ INV xbar ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>22: 85 [ = ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>23: 81 [ R/S ]</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">// Calculate r^2</span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>24: 33, 6 [ RCL 6 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>25: 55 [ × ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>26: 43 [ ( ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>27: 33, 3 [ RCL 3 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>28: 55 [ × ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>29: 89 [ xbar ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>30: 65 [ - ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>31: 33, 5 [ RCL 5 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>32: 44 [ ) ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>33: 45 [ ÷ ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>34: 43 [ ( ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>35: 33, 2 [ RCL 2 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>36: 65 [ - ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>37: 33, 1 [ RCL 1 ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>38: 55 [ × ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>39: 89 [ xbar ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>40: 85 [ = ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>41: 40 [ |x| ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>42: 81 [ R/S ]</b></span></div><div><span style="color: #2b00fe; font-family: courier; font-size: medium;"><b>43: 71 [ RST ]</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Like the TI-57, the program memory is lost when the EC 4000 is turned off. In fact, it is the only way to clear the program memory. </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Want to clear statistical memory while keeping the program memory? Press [ INV ] [ 2nd ] ( C.t ).</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Example 1:</span></div><div><span style="font-family: arial; font-size: medium;">( x, y ) Data</span></div><div><span style="font-family: arial; font-size: medium;">1: ( 5.08, 150.0 )</span></div><div><span style="font-family: arial; font-size: medium;">2: ( 5.26, 150.5 )</span></div><div><span style="font-family: arial; font-size: medium;">3: ( 5.51, 151.0 )</span></div><div><span style="font-family: arial; font-size: medium;">4: ( 5.67, 151.5 )</span></div><div><span style="font-family: arial; font-size: medium;">5: ( 5.89, 152.0 )</span></div><div><span style="font-family: arial; font-size: medium;">6: ( 6.18, 152.5 )</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Results:</span></div><div><span style="font-family: arial; font-size: medium;">a: 2.3032805</span></div><div><span style="font-family: arial; font-size: medium;">b: 138.35547</span></div><div><span style="font-family: arial; font-size: medium;">r^2: 0.993701</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Example 2:</span></div><div><span style="font-family: arial; font-size: medium;">( x, y ) Data</span></div><div><span style="font-family: arial; font-size: medium;">1: ( -2, 546 )</span></div><div><span style="font-family: arial; font-size: medium;">2: ( -1, 540 )</span></div><div><span style="font-family: arial; font-size: medium;">3: ( 0, 533 )</span></div><div><span style="font-family: arial; font-size: medium;">4: ( 1, 527 )</span></div><div><span style="font-family: arial; font-size: medium;">5: ( 2, 521 )</span></div><div><span style="font-family: arial; font-size: medium;">6: ( 3, 515 )</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Results: </span></div><div><span style="font-family: arial; font-size: medium;">a: -6.2285714</span></div><div><span style="font-family: arial; font-size: medium;">b: 533.44762</span></div><div><span style="font-family: arial; font-size: medium;">r^2: 0.999383 </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Tomorrow, more programs. I'm back to Saturday-Sunday posts. </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Take care,</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Eddie </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></div></div><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-21998766550896032272023-02-26T14:10:00.000-08:002023-04-20T12:27:43.766-07:00TI-84 Plus CE Wish List and YouTube Shorts<p><b><span style="font-family: arial; font-size: medium;">TI-84 Plus CE Wish List and YouTube Shorts</span></b></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><b><span style="font-family: arial; font-size: medium;">TI-84 Plus CE Wish List</span></b></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Disclaimer: I do not work for Texas Instruments nor do I know when (or if) TI is working on and publishing operating version 5.9, 6.0, etc. This is my opinion only (the opinion of a math and calculator enthusiast).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This focuses on the United States version of the TI-84 Plus CE series.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I would like to see the following in the next update:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. Simplification of radicals and square roots.* Currently the series only has decimal approximations.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples:</span></p><p><span style="font-family: arial; font-size: medium;">√440 returns 2 * √110</span></p><p><span style="font-family: arial; font-size: medium;">√75 + √125 returns 5 √5 + 5 √3</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. Mathematical operations returning exact results in terms of π.* Like #1, the series only has decimal approximations.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples:</span></p><p><span style="font-family: arial; font-size: medium;">In radians mode, cos^-1 (1/2) returns π/3</span></p><p><span style="font-family: arial; font-size: medium;">2 π - 3/8 * π returns 13/8 * π</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. Base mode and conversions. With the exception of the classic TI-85 and TI-86, the TI-80s do not have a base mode nor base conversions. I would like to see that added, make room under the test menu. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">4. More colors than 15 please. Maybe an RGB (red-green-blue) function in the TI-BASIC programming language? </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">With Gratitude to TI. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">YouTube Short: <a href="https://youtube.com/shorts/KOQs95qCHtg?feature=share" target="_blank">https://youtube.com/shorts/KOQs95qCHtg?feature=share</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">* FYI: #1 and #2 are available on the TI-83 CE Premium from France. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><b><span style="font-family: arial; font-size: medium;">YouTube Shorts</span></b></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">From time to time, I will post YouTube short videos (60 seconds or less) to my YouTube channel (which has been a long time starving for content):</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><a href="https://www.youtube.com/@theedspage" target="_blank"><span style="font-family: arial; font-size: medium;">https://www.youtube.com/@theedspage</span></a></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">My channel covers primarily math and calculators. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-32725054736534269792023-02-25T02:00:00.000-08:002023-04-20T12:26:10.291-07:00[チケット一般販売開始/Ticket sales started] Urban Sketching Weekend Skills Series, Tsudanuma<p></p><div style="text-align: justify;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzILokN7CAkqOygK5M1LrXyfJOh-tfOGZ9uCUj14xmygYLVz53kqNL2FWAYIx-fUoq01qtWZmhyf16MkqenTqJn63NPtWgpPVYlOeldCp5NejYD1ruldz-_7WjBiasUpeLrn28qOF7AJF-UYOSQEW4vgH0TL46_1tB_3Mna19hVMd1DcBk-Jhr9rHl_A/s1840/header-2X.jpg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="900" data-original-width="1840" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzILokN7CAkqOygK5M1LrXyfJOh-tfOGZ9uCUj14xmygYLVz53kqNL2FWAYIx-fUoq01qtWZmhyf16MkqenTqJn63NPtWgpPVYlOeldCp5NejYD1ruldz-_7WjBiasUpeLrn28qOF7AJF-UYOSQEW4vgH0TL46_1tB_3Mna19hVMd1DcBk-Jhr9rHl_A/w640-h314/header-2X.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC3npx2hxtyvltxEjaxB6WRq8BP389Vjf_XqyTup2pAUiWi7YXW8VtnaARJ19WNxmXX7XkXDma5ceOPAWxzOf_rhn2TIkbhVDKNAxNZxAA8eJZY0aNXF0OFGJQKBTUupQvOueadB63nNnEmoybnAME1Nzij3AKa9SHXyB3vBiGyf_990gohg4JXx7aqA/s1600/Event%20logo.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="772" data-original-width="1600" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC3npx2hxtyvltxEjaxB6WRq8BP389Vjf_XqyTup2pAUiWi7YXW8VtnaARJ19WNxmXX7XkXDma5ceOPAWxzOf_rhn2TIkbhVDKNAxNZxAA8eJZY0aNXF0OFGJQKBTUupQvOueadB63nNnEmoybnAME1Nzij3AKa9SHXyB3vBiGyf_990gohg4JXx7aqA/s320/Event%20logo.jpg" width="320" /></a></div><div><br /></div><div>これまでのイベント情報は<a href="https://urbansketchers-japan.blogspot.com/search/label/Urban%20Sketching%20Weekend" target="_blank">こちら</a>からチェックできます。</div><div>You can check out the information on the event and instructors <a href="https://urbansketchers-japan.blogspot.com/search/label/Urban%20Sketching%20Weekend" target="_blank">here</a>.</div><h3 style="text-align: left;">チケット一般販売開始しました!/Ticket sales has just started!</h3><p>2月25日(土)19時(日本時間)より、チケットの一般販売を開始しました。<br />以下のPeatixのチケット販売ページからご希望のチケットをご購入ください。<br /><a href="https://uskweekend-tsudanuma.peatix.com/" target="_blank">https://uskweekend-tsudanuma.peatix.com/</a><br /></p><p>General ticket sales started at 7pm on February 25 (Sat) (JST).<br />Please check out the ticket sales page on Peatix and make a purchase.<br /><a href="https://uskweekend-tsudanuma.peatix.com/" target="_blank">https://uskweekend-tsudanuma.peatix.com/</a></p><p><b>●購入時の注意/Notes on purchase</b></p><p><span style="color: red;">同時間帯に開催する複数プログラムに参加することはできないため、購入時にタイムテーブルをよくご確認ください。<br />また、ロブ・スケッチャーマンおよびケーシー・トリウミのデモは、ワークショップ券購入の有無によって金額が異なります(購入者・各1,000円/非購入者・各2,000円)。購入時にお間違えのないよう、ご注意ください。ワークショップ券非購入にもかかわらず購入者価格を選択された方へは追加請求させていただきます。</span></p><p><span style="color: red;">Be sure to check the timetable carefully when you make a purchase since you cannot participate in activities that happen in the same time slot.<br />Also, the ticket prices for the demos by Rob Sketcherman and Casey Toriumi will be different depending on whether you are a workshop ticket holder or not (1,000 yen each for ticket holders / 2,000 yen for non-ticket holders). Be sure to check the price before purchasing. If you are a non-workshop ticket holder and purchase a demo ticket for ticket holders, the difference will be charged.</span></p><p><br /></p><p>お問合せはチケット販売ページから直接行っていただくか、Urban Sketchers Japanのメールアドレス(<span style="color: #2b00fe;">uskjapanevent@gmail.com</span>)へご連絡ください。<br />皆様のご参加をお待ちしております。どうぞ宜しくお願いいたします。</p><p>For queries, contact us through the ticket sales page or send a message to <span style="color: #2b00fe;">uskjapanevent@gmail.com</span>.<br />We are looking forward to seeing you at the event.</p><p><br /></p>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-19927834886229622322023-02-25T00:00:00.000-08:002023-04-20T12:27:44.011-07:00HP 12C: The C Indicator - Odd Period (Calculating Payment)<p><span style="font-family: arial;"><b>HP 12C: The C Indicator - Odd Period (Calculating Payment)</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>There is a C indicator on my HP 12C!</b></span></p><p><span style="font-family: arial;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizV5awAJKCzmUfzdndDxmlj_4j9lW2RdxSORXHbF-0Pd_OZqIwDKTegavNlFIJfitft_LKpJuuj3ZWLoJIlQvMzI3y7yhNhQadsXjLKOm0EUTa1FE3hxk_3s2OiilHO1cVRivneY1GSWZVSkPNXX9C2HVCgMHo8ETxKwZIj1VcJAYs5dFfV0vT6Lmk/s4624/HP%2012C%20C%20indicator.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3468" data-original-width="4624" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizV5awAJKCzmUfzdndDxmlj_4j9lW2RdxSORXHbF-0Pd_OZqIwDKTegavNlFIJfitft_LKpJuuj3ZWLoJIlQvMzI3y7yhNhQadsXjLKOm0EUTa1FE3hxk_3s2OiilHO1cVRivneY1GSWZVSkPNXX9C2HVCgMHo8ETxKwZIj1VcJAYs5dFfV0vT6Lmk/w640-h480/HP%2012C%20C%20indicator.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">When I bought a HP 12C calculator that was manufactured in Brazil, there was a C indicator on it. It was an odd-period calculation switch that has been a documented feature of the HP 12C. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Odd Period of an Annuity </b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">An odd period of any annuity occurs when the present value (example: loan proceeds) is received before the first period (example: month) occurs. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">On the diagram below:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">PV: proceeds received</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">PV0: balance at the start of the first period. This the proceeds plus any interest accrued during the odd period. In general, PV0 > PV. </span></p><p><span style="font-family: arial;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpVtuauJ2guBBScmN8xQGQ0uqO-NijVhEhF26za6AiVzpbg9OOe3U2fSDB5pf3BF1nmXzH0oQSi_H1hxir2OmtHLuvEAYh623OuPA6ZiUxguBNbyvNQDVbEcDXM_0gaxGa95ahOGEZu3zGp9WTXTz41dJn9owTA9nU49AkPD7U_vrOuP_au3iUTzX2/s740/Monthly%20payment%20of%20a%20loan%20at%20%20the%20end%20of%20each%20month.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="421" data-original-width="740" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpVtuauJ2guBBScmN8xQGQ0uqO-NijVhEhF26za6AiVzpbg9OOe3U2fSDB5pf3BF1nmXzH0oQSi_H1hxir2OmtHLuvEAYh623OuPA6ZiUxguBNbyvNQDVbEcDXM_0gaxGa95ahOGEZu3zGp9WTXTz41dJn9owTA9nU49AkPD7U_vrOuP_au3iUTzX2/w640-h364/Monthly%20payment%20of%20a%20loan%20at%20%20the%20end%20of%20each%20month.jpg" width="640" /></a></div><br /><p><span style="font-family: arial;">For example: loan proceeds of $10,000 is received on March 26, 2022 (the PV), with the first payment due at the end of the next month, April 30, 2022. In this case, the loan proceeds were received five days before the "official" first month of the loan which starts on April 1, 2022. The odd period is 5 days, or 5/30 of a month.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">In general, all months are considered to be 30 days under a 30/360 calendar system. You can use the actual calendar (365/366-day year) if you wish. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">To account for an odd period, add the fractional part of the odd period to the number of payments and store it the [ n ] variable. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">There are two ways to calculate odd period interest: simple interest and compound interest.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial;"><b>HP 12 Settings for Odd Period Interest</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">C indicator: the odd period interest is calculated using compound interest</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">No C indicator: the odd period interest is calculated using simple interest</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The setting is set by pressing [ STO ] [ EEX ].</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial;"><b>Casio FC-200V Settings for Odd Period Interest</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The Casio FC-200V (and FC-100V (1st and 2nd editions)) has a setting for odd periods. In the Compound Interest app (CPMD), press [ SETUP ] and select dn, then select between CI and SI. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">CI: the odd period interest is calculated using compound interest</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">SI: the odd period interest is calculated using simple interest</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">This set up is also present in the Simple Interest app (SMPL).</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial;"><b>Formulas</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">If your calculator doesn't have odd period settings, you will need to calculate PV0. Once PV0 is calculated, then proceed to calculate payment, ignoring the odd value for n. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Compound Interest:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">PV0 = PV × (1 + I%÷(n×100))^(odd period)</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Compound Interest - Monthly Payment, 30/360 Day Calendar:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">PV0 = PV × (1 + I%÷(1200))^(days ÷ 30)</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Simple Interest:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">PV0 = PV × (1 + I% ÷ 100 × odd period)</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Compound Interest - Monthly Payment, 30/360 Day Calendar:</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">PV0 = PV × (1 + I% × days ÷ 36000)</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">where:</span></p><p><span style="font-family: arial;">PV = proceeds</span></p><p><span style="font-family: arial;">PV0 = balance at the beginning of the first period</span></p><p><span style="font-family: arial;">I% = annual interest rate (not converted to decimal)</span></p><p><span style="font-family: arial;">odd period = fraction of the year which the odd period represents</span></p><p><span style="font-family: arial;">days = days of the odd period</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">These formulas assume end-of-period payments, but also work equally as well for beginning-of-period payments. In practice the difference between the two methods result in a small difference.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Example</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Facts:</span></p><p><span style="font-family: arial;">* Loan proceeds: $17,755.00</span></p><p><span style="font-family: arial;">* Interest rate: 7%</span></p><p><span style="font-family: arial;">* Number of monthly payments: 60, payments are due at the end of the month</span></p><p><span style="font-family: arial;">* Odd period: 15 days, 30/360 calendar</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Find the payment.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial;"><b>Compound Interest</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">HP 12C: press [ STO ] [ EEX ] until the C indicator is on</span></p><p><span style="font-family: arial;">[ f ] [ x<>y ] (CLEAR FIN)</span></p><p><span style="font-family: arial;">[ g ] (END)</span></p><p><span style="font-family: arial;">60.5 [ n ]</span></p><p><span style="font-family: arial;">7 [ g ] (12÷)</span></p><p><span style="font-family: arial;">17755 [ PV ]</span></p><p><span style="font-family: arial;">[ PMT ] returns -352.59</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Casio FC-200V: set dn to CI</span></p><p><span style="font-family: arial;">[ CMPD ]</span></p><p><span style="font-family: arial;">Set: End</span></p><p><span style="font-family: arial;">N = 60.5</span></p><p><span style="font-family: arial;">I% = 7</span></p><p><span style="font-family: arial;">PV = 17755</span></p><p><span style="font-family: arial;">P/Y = 12, C/Y = 12 </span></p><p><span style="font-family: arial;">Solve PMT for -352.59</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Others:</span></p><p><span style="font-family: arial;">PV0 = 17755 × (1 + 7 × 15 ÷ 36000)= 17806.71</span></p><p><span style="font-family: arial;">N = 60</span></p><p><span style="font-family: arial;">I%/YR = 7</span></p><p><span style="font-family: arial;">PV = 17806.79</span></p><p><span style="font-family: arial;">P/Y = 12, C/Y = 12</span></p><p><span style="font-family: arial;">Solve PMT for -352.59</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial;"><b>Simple Interest</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">HP 12C: press [ STO ] [ EEX ] until the C indicator is off</span></p><p><span style="font-family: arial;">[ f ] [ x<>y ] (CLEAR FIN)</span></p><p><span style="font-family: arial;">[ g ] (END)</span></p><p><span style="font-family: arial;">60.5 [ n ]</span></p><p><span style="font-family: arial;">7 [ g ] (12÷)</span></p><p><span style="font-family: arial;">17755 [ PV ]</span></p><p><span style="font-family: arial;">[ PMT ] returns -352.60</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Casio FC-200V: set dn to SI</span></p><p><span style="font-family: arial;">[ CMPD ]</span></p><p><span style="font-family: arial;">Set: End</span></p><p><span style="font-family: arial;">N = 60.5</span></p><p><span style="font-family: arial;">I% = 7</span></p><p><span style="font-family: arial;">PV = 17755</span></p><p><span style="font-family: arial;">P/Y = 12, C/Y = 12 </span></p><p><span style="font-family: arial;">Solve PMT for -352.60</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Others:</span></p><p><span style="font-family: arial;">PV0 = 17755 × (1 + 7÷1200)^(15 ÷ 30) = 17806.79</span></p><p><span style="font-family: arial;">N = 60</span></p><p><span style="font-family: arial;">I%/YR = 7</span></p><p><span style="font-family: arial;">PV = 17806.71</span></p><p><span style="font-family: arial;">P/Y = 12, C/Y = 12</span></p><p><span style="font-family: arial;">Solve PMT for -352.60</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">As you can see, little, if any difference between the two methods.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Are there are any other calculators that can handle odd-period calculations?</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">I'm hesitant to say yes. How do we know if a finance calculator or the finance mode of a scientific or graphing calculator has handles odd-period calculations? Check the set up or mode settings. If you see an option to set odd periods to simple interest or compound interest, then yes. If not, use the formulas stated above to first calculate PV0 and proceed. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">For the record, neither the Texas Instruments BA II Plus nor the Sharp EL-738F do not have not odd-period calculation settings. No graphing calculator or scientific calculator with time value of money modules has this that I know of. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">On the Calculated Industries Qualifier Plus IIIFX, use the PV0 amount for the Loan Amount. This calculator can find the prepaid interest, which is based on 30/360 day year, simple interest. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Sources</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><u>HP 12C Financial Calculator User's Guide</u>. Hewlett Packard. Edition 5. San Diego, California, United States. 2008. pp. 50-53</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><u>FC-200V, FC-100V (2nd Edition/Financial Consultant User's Guide</u>. Casio. Shibuya-ku, Tokyo, Japan. 2021</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">I will back to the Saturday-Sunday schedule starting on March 4, 2023. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Eddie</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-44878695122147335622023-02-24T18:24:00.000-08:002023-04-20T12:26:10.533-07:00[よくある質問/FAQ] Urban Sketching Weekend Skills Series, Tsudanuma<p> </p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp5nupMSvL5_b2sFQsP5A6-HDAPLCaKpKlCwzTaHFIGev-U7SY6n3pR-QZKnva7lpOEGLMC2RaI_uveLJPkgq77IlYTAbRc5pOEz9eygnQyrlo36Oqh2sXFGYJY7Ea4ENEWDfKFlDzyK8JQyzZ7caetHPZwH_gyWvNIDHrTIG4zZMLenw_5-1zOP0xXw/s1600/Event%20logo.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="772" data-original-width="1600" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp5nupMSvL5_b2sFQsP5A6-HDAPLCaKpKlCwzTaHFIGev-U7SY6n3pR-QZKnva7lpOEGLMC2RaI_uveLJPkgq77IlYTAbRc5pOEz9eygnQyrlo36Oqh2sXFGYJY7Ea4ENEWDfKFlDzyK8JQyzZ7caetHPZwH_gyWvNIDHrTIG4zZMLenw_5-1zOP0xXw/w400-h193/Event%20logo.jpg" width="400" /></a></div><br /><p></p><h3 style="text-align: left;">よくある質問/FAQ</h3><p>質問と回答は随時更新していきます。<br />English follows. This page will be updated as needed.</p><p><b>Q1: 同時間帯に行うデモとワークショップの両方に出たいです。デモ終了後、ワークショップに途中参加できますか?</b><br />A1:ワークショップへの途中参加はできません(やむを得ない事情で遅刻した場合は除きます)。恐れ入りますが、デモかワークショップのいずれかを選択してください。</p><p><b>Q2:4月1日(土)のロブのデモ、フリースケッチセッション、ベンのワークショップのすべてに参加したいですが、可能ですか?</b><br />A2:ロブのデモとフリースケッチセッションはともに14:30開始、ベンのワークショップは16時開始です。フリースケッチセッションに参加できる時間はありません。ロブのデモとベンのワークショップのみとしてください。</p><p><b>Q3:参加者が画材を用意する必要はありますか?</b><br />A3:画材はご自身でご用意ください。ワークショップでは内容によって必要な画材が異なるため、<a href="https://uskj202304.webflow.io/" target="_blank">こちら</a>で事前に持ち物をご確認ください。スケッチャウォーク、フリースケッチセッション、ドリンク&ドローではお好みの画材をご使用ください。</p><p><b>Q4:ゴミは捨てられますか?</b><br />A4:ゴミは各自お持ち帰りください。ベンのワークショップで食事を提供しますが、その際に出る紙皿等のゴミのみこちらで回収します。</p><p><b>Q5:本部会場はどこですか?また本部への道順を教えてください。</b><br />A5:本部は丸田集会所です。道順は<a href="https://drive.google.com/file/d/1S5UK1hpsXo5T_k79BOn62FtzzbiX8nTh/view?usp=share_link" target="_blank">こちら</a>からご確認ください。4月2日(日)17時以降のみ、丸田集会所が閉まり、みはし湯ホールが集合場所になります。</p><p>---------------------<br /><b>Q1: I want to participate in both demo and workshop happening in the same timeslot. Can I join the workshop part way through after the demo?</b><br />A1: You cannot join a workshop part way through (except the case in which you are late for an unavoidable reason). Choose either demo or workshop.</p><p><b>Q2: Is it possible to take Rob's demo, free sketch session, and Ben's workshop on April 1?</b><br />A2: Both of Rob's demo and the free sketch session start at 2.30, and Ben's workshop at 4, which means you will not have time to join the free sketch session. Take Rob's demo and Ben's workshop only.</p><p><b>Q3: Do I need to bring sketching tools?</b><br />A3: Yes, you do. Required tools are different depending on the workshop, so please check out what to bring <a href="https://uskj202304en.webflow.io/" target="_blank">here</a>. You can use tools you like in the sketchwalk, free sketch session, and drink & draw.</p><p><b>Q4: Can I throw away trash in the venues?</b><br />A4: No, please take your trash with you. We will only collect trash such as paper trays used to eat dishes served for Ben's workshop. </p><p><b>Q5: Where is the event hub? How can I get there?</b><br />A5: The hub is Maruta Meeting Room. Check out the directions <a href="https://drive.google.com/file/d/1S5UK1hpsXo5T_k79BOn62FtzzbiX8nTh/view?usp=share_link" target="_blank">here</a>. Only after 5pm on April 2, Maruta Meeting Room will be closed and Mihashiyu Hall will be the meeting point.</p>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0tag:blogger.com,1999:blog-3749079740372415001.post-57278342483661864522023-02-22T16:56:00.000-08:002023-04-20T12:26:10.779-07:00[インストラクター紹介4/Meet our instructors 4] Urban Sketching Weekend Skills Series, Tsudanuma<p> </p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi43WpKjZw7mObYL8FXec4QcxNEuS2L3PpLkKb1Dadiz8ch0i9Q7s2Ull5VUlLkQ2VB0Lj6ygeJtI9TFUBtkoH8d5Dm2JTrJepEwMPTgYGL1uYvMneq3YbNGSNppMCghYOlXqBJ9TipaWvX1Yh3oI1umhb7hG6D5agpRmF6lSbfS_ar4-H6ZukyZwmY3w/s4096/Kumi.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1562" data-original-width="4096" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi43WpKjZw7mObYL8FXec4QcxNEuS2L3PpLkKb1Dadiz8ch0i9Q7s2Ull5VUlLkQ2VB0Lj6ygeJtI9TFUBtkoH8d5Dm2JTrJepEwMPTgYGL1uYvMneq3YbNGSNppMCghYOlXqBJ9TipaWvX1Yh3oI1umhb7hG6D5agpRmF6lSbfS_ar4-H6ZukyZwmY3w/w640-h244/Kumi.JPG" width="640" /></a></div><br /><p></p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibZsRHzQ7K1VrEhFCs1uHIMKMYAX8Iinqdr9EC1fR2miWpWVVU47zEAZ_q1OzWWx2YstSTAXObvaIurfpZ7cMH73AN_qKWYTD9iycGUikRa_GlV6cr86jik1O2LUo4Y7YbwS0ES1O3m8vRf3Nwd8tYBg1FSjtQJ8Ib_OoGEa5viPH8GHjzdVBHW_AE4g/s1600/Event%20logo.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="772" data-original-width="1600" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibZsRHzQ7K1VrEhFCs1uHIMKMYAX8Iinqdr9EC1fR2miWpWVVU47zEAZ_q1OzWWx2YstSTAXObvaIurfpZ7cMH73AN_qKWYTD9iycGUikRa_GlV6cr86jik1O2LUo4Y7YbwS0ES1O3m8vRf3Nwd8tYBg1FSjtQJ8Ib_OoGEa5viPH8GHjzdVBHW_AE4g/w400-h193/Event%20logo.jpg" width="400" /></a></div><br /><h3 style="text-align: left;">チケット販売情報/Ticket sales info</h3><p style="text-align: left;">たいへんお待たせしておりますチケット販売ですが、用意が整いましたので、順次販売を開始します。チケット販売には<a href="https://peatix.com/" target="_blank">Peatix</a>を使用します。<br /><b>・2月23日(木)19時(日本時間):先行販売開始<br /></b>事前にアンケートに回答いただいた方より先行販売いたします。アンケート回答時にお知らせいただいたメールアドレスまたはInstagramのアカウントに、Urban Sketchersよりチケット販売ページのお知らせをお送りいたします。<br /><b>・2月25日(土)19時</b><b>(日本時間):一般発売開始<br /></b>当ブログ、<a href="https://www.facebook.com/groups/194952257673256/" target="_blank">Facebook</a>、<a href="https://www.instagram.com/uskjapan/" target="_blank">Instagram</a>よりチケット販売ページをお知らせいたします。</p><p style="text-align: left;">We're starting ticket sales on <a href="https://peatix.com/" target="_blank">Peatix</a> as follow:<br /><b>- 7pm, February 23 (Thu) (JST): Pre-sales starts<br /></b>Pre-sales for those who have answered the questionnaire. We'll send a message from Urban Sketchers Japan's email address or Instagram to an email address or Instagram account we collected through the questionnaire to notify the ticket sales page.<br /><b>- 7pm, February 25 (Sat) (JST): General sales starts</b><br />We'll announce the ticket sales page on this blog, our <a href="https://www.facebook.com/groups/194952257673256/" target="_blank">Facebook </a>and <a href="https://www.instagram.com/uskjapan/" target="_blank">Instagram</a>.</p><p><b>定員/Capacity</b></p><p></p><ul style="text-align: left;"><li>ワークショップ:各15名/Workshop: 15 persons each</li><li>デモ:各20名/Demos: 20 persons each</li><li>スケッチウォーク・お土産バッグの個数:40個/Souvenir bags accompanied with sketchwalk: 40 bags<br /><div dir="auto" style="animation-name: none; background-color: white; color: #050505; font-family: "Segoe UI Historic", "Segoe UI", Helvetica, Arial, "hiragino kaku gothic pro", meiryo, "ms pgothic", sans-serif; font-size: 15px; transition-property: none; white-space: pre-wrap;">★お土産バッグは4/2のスケッチウォークに参加できない方や、申し込みに間に合わなかった方向けに少量ですが現地販売も検討しています。</div><div dir="auto" style="animation-name: none; background-color: white; color: #050505; font-family: "Segoe UI Historic", "Segoe UI", Helvetica, Arial, "hiragino kaku gothic pro", meiryo, "ms pgothic", sans-serif; font-size: 15px; transition-property: none; white-space: pre-wrap;">★We might prepare the limited number of souvenir bags to sell on site, mainly for those who can't make it on April 2.</div></li></ul><p></p><p style="text-align: left;"><br /></p><h3 style="text-align: left;">インストラクター紹介4/Meet our instructors 4</h3><p><b>松川久美/Kumi Matsukawa</b>(Instagram:@<a href="https://www.instagram.com/kumimatsukawaart/" target="_blank">kumimatsukawaart</a>)</p><p>さて、最後に紹介するインストラクターは、われらがUrban Sketchers Japanの創設者、松川久美さんです!もはや説明不要かと思いますが、Urban Sketchers初期の頃から東京のスケッチャー代表として活躍されてきた方です。<br />Finally, we'll introduce Kumi Matsukawa, the founder of Urban Sketchers Japan! She's been an international blog correspondent from Tokyo for Urban Sketchers since the early days of the community.</p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNBd6_BlZENluR1Kc239SzRcxZpqgXD1Dhzn1Yoo6Fnl8XTcUmTKWT8zaaYG0RdMP8fkzmShKlFvLbMHy2rOHz1ZNc0MnL1tSMqaGJktDBhSz1vebc9cLh3KcC03u_N1VR_-UWt3jdcbeamFUnVTRaIUfAizPozVnnvIIyfETmHZHeSoRg-tWxiK3DdA/s960/47559391912_8b7e4644d0_o.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="686" data-original-width="960" height="229" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNBd6_BlZENluR1Kc239SzRcxZpqgXD1Dhzn1Yoo6Fnl8XTcUmTKWT8zaaYG0RdMP8fkzmShKlFvLbMHy2rOHz1ZNc0MnL1tSMqaGJktDBhSz1vebc9cLh3KcC03u_N1VR_-UWt3jdcbeamFUnVTRaIUfAizPozVnnvIIyfETmHZHeSoRg-tWxiK3DdA/s320/47559391912_8b7e4644d0_o.jpg" width="320" /></a></div><br /><p>久美さんは水彩、マーカー、パステルなど様々な画材・画法を横断して描く多彩なスケッチャーですが、今回のイベントでは基礎的な水彩スケッチのワークショップを行います。スケッチを始めたばかりだと、まず構図のとり方や陰影のつけ方がわからず戸惑ってしまいますよね。久美さんのワークショップでは、対象のサイズやバランスを正確に捉える方法、明暗や奥行きの理解、水彩での基本的な表現を、サムネイル画(練習用の小さいサイズのスケッチ)を活用した実践を通して学ぶことができます。その際にキーワードになるのが、"wink and squint"(目を細めて見る)。「こんなの描けない!」と圧倒されてしまう景色も、まず目を細めてよく観察することで正確な構図と陰影を理解するヒントが見つかるはずです。<br />Kumi-san is a versatile sketcher who handles different mediums and methods, including watercolor, markers, and pastel painting. But, in this event, she will give a workshop on basic watercolor sketching. It's not easy to compose your subject with correct proportion and give your drawings depth in the beginning. Through Kumi-san's workshop, participants can practice using thumbnail drawing and learn to capture accurate proportions, understand depth and contrast in value, and apply watercolor. Here, the key is "wink and squint". Even if you're overwhelmed by the view in front of you that feels too complicated for you, you can appreciate what you see more by narrowing your eyes and observing attentively, which will lead to better composition and comprehension of value. </p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnkPdjR8miHoMrpuT1HC9yEBcreoSNDnHE8v7C-bKsVtgzFUBouvlDJTxxCLSywSJQowxcVn8errSsjjipSHmIVYA-V1BhgP14zcHZuY5jyIUM8JSbuRInbfDU4kCi6LQMJjM7M6TlfBmDOz7o3jHs0Ab887mEjdtJTiujcn4E7BdzKUh6usVZVo53RQ/s4032/IMG-4237.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnkPdjR8miHoMrpuT1HC9yEBcreoSNDnHE8v7C-bKsVtgzFUBouvlDJTxxCLSywSJQowxcVn8errSsjjipSHmIVYA-V1BhgP14zcHZuY5jyIUM8JSbuRInbfDU4kCi6LQMJjM7M6TlfBmDOz7o3jHs0Ab887mEjdtJTiujcn4E7BdzKUh6usVZVo53RQ/s320/IMG-4237.jpg" width="240" /></a></div><p><br /><プログラム情報/Activity info></p><p><b>ワークショップ(講師:松川久美) @菊田神社・菊田水鳥公園(<a href="https://www.google.com/maps/place/%E8%8F%8A%E7%94%B0%E7%A5%9E%E7%A4%BE/@35.6842402,140.0257099,18z/data=!4m5!3m4!1s0x6022802dd078b5cf:0x26fcd8812e426b89!8m2!3d35.6845275!4d140.0272515?coh=164777&entry=tt&shorturl=1" target="_blank">Google map</a>)<br />Workshop by Kumi Matsukawa @Kikuta Shirine and Kikuta Mizudori Park (<a href="https://www.google.com/maps/place/%E8%8F%8A%E7%94%B0%E7%A5%9E%E7%A4%BE/@35.6842402,140.0257099,18z/data=!4m5!3m4!1s0x6022802dd078b5cf:0x26fcd8812e426b89!8m2!3d35.6845275!4d140.0272515?coh=164777&entry=tt&shorturl=1" target="_blank">Google map</a>)</b><br />- 4月1日(土)10時~13時 /10am - 1pm, April 1 (Sat)<br />- チェックイン場所:丸田集会所(<a href="https://goo.gl/maps/Bu2rUZbxJpKZvYd76" target="_blank">Google map</a>)/Check-in site: Maruta Meeting Room (<a href="https://goo.gl/maps/Bu2rUZbxJpKZvYd76" target="_blank">Google map</a>)<br />- 持ち物:水彩絵の具、筆または水筆、色鉛筆、水彩画に使用できる紙・スケッチブック、ペン(任意) <br />- Supply list: watercolor, brushes or waterbrushes, colored pencils, paper/sketchbook suitable for watercolor use, pens (optional)<br />*開始30分前までにチェックイン場所にお越しください。<br />*Be sure to arrive at the check-in site by 30 minutes before the activity starts.</p><p>-------<br />タイムテーブル/Timetable<br /><a href="https://drive.google.com/file/d/18_Glf1pHNNwJyV3GYYSi7hSXMTsKEoC6/view?usp=share_link" target="_blank">https://drive.google.com/file/d/18_Glf1pHNNwJyV3GYYSi7hSXMTsKEoC6/view?usp=share_link</a><br /></p><p>価格表/Price list<br /><a href="https://drive.google.com/file/d/1X5PtlE-2PF7r8e_CLeohRQCqGUfgJtUb/view?usp=share_link" target="_blank">https://drive.google.com/file/d/1X5PtlE-2PF7r8e_CLeohRQCqGUfgJtUb/view?usp=share_link</a><br /></p><p><br /></p><div><br /></div>Jokka Johttp://www.blogger.com/profile/01904172572211369691noreply@blogger.com0