Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
01-10-2021, 04:17 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,251 Joined: Dec 2013
Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
Introduction

The program ESGRAPH plots the parametric equations containing integrals:

x(t) = ∫(cos f(x) dx, x = 0 to t)
y(t) = ∫(sin f(x) dx, x = 0 to t)

The program uses f(x) = a*x^p

When p = 2, the curve is a Euler Spiral (see source).

Casio fx-9750GIII Program: ESGRAPH
Code:
 ' 2020-12-22 EWS Rad ' L1, X L2, Y "F = A×X^P" "FACTOR"?→A "P=2, EULER SPIRAL" "POWER"?→P ∫(A×cos(X^P),0,-2π)→X ∫(A×sin(X^P),0,-2π)→Y {X}→List 1 {Y}→List 2 Menu "π÷R?","8",A,"16",B,"32",C Lbl A: 8 → R: Goto 0 Lbl B: 16 → R: Goto 0 Lbl C: 32 → R : Goto 0 Lbl 0 For -2π+π÷R→T To 2π Step π÷R ∫(A×cos(X^P),0,-2π)→X ∫(A×sin(X^P),0,-2π)→Y Augment(List 1, {X})→List 1 Augment(List 2, {Y})→List 2 (T+2π)÷(4π)×100→G RndFix(G,0)→G Locate 1,7,"PROGRESS:    %" Locate 11,7,G Next S-Gph1 DrawOn, xyLine, List 1, List 2, 1, Dot DrawStat
Havil, Julian. Curves for the Mathematical Curious: An Anthology of the Unpredictable, Historical, Beautiful, and Romantic Princeton Universal Press. Princeton and Oxford. Princeton, NJ 2019 ISBN 978-0-691-18005-2

For examples and more details, visit my blog at Eddie's Math and Calculator blog: http://edspi31415.blogspot.com/2021/01/c...etric.html
01-14-2021, 04:30 PM
Post: #2
 Hlib Member Posts: 242 Joined: Jan 2015
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
CASIO`s 20-year-old graphing calculators can handle this example. What does 9750GIII have to do with it? Is that a demonstration of the new Menu function, which was introduced in the TI calculators back in 1994?
01-16-2021, 03:15 PM
Post: #3
 Eddie W. Shore Senior Member Posts: 1,251 Joined: Dec 2013
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
The fx-9750GIII was the calculator I used for this particular post. Of course it isn't the only calculator that this can be done on?
01-17-2021, 03:34 AM
Post: #4
 Nad Junior Member Posts: 42 Joined: Nov 2019
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
(01-16-2021 03:15 PM)Eddie W. Shore Wrote:  The fx-9750GIII was the calculator I used for this particular post.

Thanks for sharing, your posts are always informative and fun to read

Everything will be alright in the end. If it's not alright, then it's not the end.
01-17-2021, 08:29 AM
Post: #5
 EdS2 Senior Member Posts: 346 Joined: Apr 2014
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
(01-16-2021 03:15 PM)Eddie W. Shore Wrote:  The fx-9750GIII was the calculator I used for this particular post.

Thanks for sharing, your posts are always informative and fun to read

"for the Mathematically Curious" is a nice qualifier! (From the citation in the article)
01-17-2021, 06:56 PM
Post: #6
 Benjer Member Posts: 50 Joined: Apr 2017
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral

Chiming in to agree. I never read a post at your blog I didn't like.
01-17-2021, 07:49 PM
Post: #7
 davej Junior Member Posts: 5 Joined: Jan 2020
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
Thanks for sharing this - I just picked up the Fx-9750GIII , mostly for the python support. Its been fun to play with.

I did enter the program for the ESGraph Plots from your post and initially had an issue when it came to plotting the values.

I think the for loop needs to have the integrals for X,Y vary by the step value defined for T - Basically if you change ∫(A×cos(X^P),0,-2π)→X to ∫(A×cos(X^P),0,T)→X and ∫(A×sin(X^P),0,-2π)→Y to ∫(A×sin(X^P),0,T)→Y I get the graphs shown on your blog.

Apologies if this was obvious to all.

Thanks and regards for making the effort - I do enjoy reading your posts here and on your blog.

Dave
01-17-2021, 08:16 PM (This post was last modified: 01-17-2021 08:17 PM by Steve Simpkin.)
Post: #8
 Steve Simpkin Senior Member Posts: 633 Joined: Dec 2013
RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
(01-17-2021 07:49 PM)davej Wrote:  Thanks for sharing this - I just picked up the Fx-9750GIII , mostly for the python support. Its been fun to play with.

I did enter the program for the ESGraph Plots from your post and initially had an issue when it came to plotting the values.

I think the for loop needs to have the integrals for X,Y vary by the step value defined for T - Basically if you change ∫(A×cos(X^P),0,-2π)→X to ∫(A×cos(X^P),0,T)→X and ∫(A×sin(X^P),0,-2π)→Y to ∫(A×sin(X^P),0,T)→Y I get the graphs shown on your blog.

Apologies if this was obvious to all.

Thanks and regards for making the effort - I do enjoy reading your posts here and on your blog.

Dave

It should also be noted that KhiCAS is now available on the Casio Fx-9750GIII (thank you Parisse!) giving it a CAS that is similar to the one in the HP Prime (same Xcas engine).
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