Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral

[Eddie W. Shore]

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

[Hlib]

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?

[Eddie W. Shore]

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?

[Nad]

(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

[EdS2]

(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)

[Benjer]

(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.

[davej]

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

[Steve Simpkin]

(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