+- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: Not HP Calculators (/forum-7.html) +--- Forum: Not remotely HP Calculators (/forum-9.html) +--- Thread: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral (/thread-16155.html) Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Eddie W. Shore - 01-10-2021 04:17 PM 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/casio-fx-9750giii-trigonometric.html RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Hlib - 01-14-2021 04:30 PM 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? RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Eddie W. Shore - 01-16-2021 03:15 PM 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? RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Nad - 01-17-2021 03:34 AM (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 RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - EdS2 - 01-17-2021 08:29 AM (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) RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Benjer - 01-17-2021 06:56 PM (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. RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - davej - 01-17-2021 07:49 PM 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 RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Steve Simpkin - 01-17-2021 08:16 PM (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.php?p=286192&sid=ffa4b529c51b2cba300c57c7076ed783#286192