/
hyperspherevols.wxm
121 lines (91 loc) · 2.6 KB
/
hyperspherevols.wxm
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/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 12.04.0 ] */
/* [wxMaxima: title start ]
Volumes of Hyperspheres
[wxMaxima: title end ] */
/* [wxMaxima: input start ] */
svol(d):=%pi^(d/2)/(d/2)!;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(1);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(2);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(3);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(4);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(5);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(6);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(7);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(8);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
wxplot2d(svol(d),[d,0,20]);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
wxplot2d(log(svol(d)),[d,0,200]);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
solve(diff(svol(d),d)=0);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
wxplot2d(svol(d),[d,5.2,5.3]);
/* [wxMaxima: input end ] */
/* [wxMaxima: subsect start ]
four ways of saying the same thing
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
(1/2)!;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
0.5!;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
float(sqrt(%pi)/2);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
gamma(1.5);
/* [wxMaxima: input end ] */
/* [wxMaxima: subsect start ]
and thus, another hypersphere-volume formula
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
svol(d):= %pi^(d/2)/gamma(d/2+1);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(1);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
although I like
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
(tau/2)^(d/2)/(d/2)!;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(d+1)/svol(d);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
minfactorial(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
factcomb(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(3)/svol(2);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
svol(4)/svol(3);
/* [wxMaxima: input end ] */
/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$