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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
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?
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?
(01-16-2021 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
(01-17-2021 03:34 AM)Nad Wrote: [ -> ]
(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 03:34 AM)Nad Wrote: [ -> ]Thanks for sharing, your posts are always informative and fun to read

Chiming in to agree. I never read a post at your blog I didn't like.
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 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).
https://www.cemetech.net/forum/viewtopic...783#286192
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