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
' 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
Notes:
* There are four spaces between PROGRESS: and %. This progress meter is to inform the user of the program's completion.
* The characters % and ', percent sign and apostrophe respectively, are found on the program editing default menu (TOP, BTM, SRC, MENU, A ←→a, CHAR), by pressing [F6] (CHAR), [F2] (SYBL)
* Everything that follows an apostrophe is a comment and can be left out.
* The range of -2π to 2π is used.
* The lower the precision, the faster the graph is made but accuracy of the graph is sacrificed. In a lot of cases, patience is required.
* P is a positive integer.
Examples
Example 1: Euler Spiral: A = 1/2, P = 2, precision 32
Example 2: A = 1, P = 3, precision 32
Example 3: A = 2, P = 1, precision 16
Source:
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
Eddie
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