It loses accuracy somewhere between n=150 and n=200. Keep in mind though that the dimensions of these "volumes" are not comparable.
Each "n-volume" of dimension n-1 is "paper thin (or thinner)" than the "n-volume" of dimension n. That said, I have not sat down and verified the results by hand, I'm just trusting that the equation is accurate (though it seems to be). See also: https://en.wikipedia.org/wiki/Volume_of_an_n-ball Thanks, -- Raul On Tue, Aug 15, 2017 at 4:18 PM, Jan-Pieter Jacobs <[email protected]> wrote: > Nice sentence. > > Is it accurate for higher dimensions too? To me it seems a bit > counterintuitive that after n=6, the n-volume rapidly declines until almost > zero. > > For instance: > load 'plot' > plot 1 sphvol i. 100 > > Best regards, > > Jan-Pieter > > On 15 Aug 2017 7:55 p.m., "Raul Miller" <[email protected]> wrote: > >> sphvol=: (1p1&^%!)@-:@] * ^ >> 1 sphvol 3 >> 4.18879 >> 1 sphvol i.7 >> 1 2 3.14159 4.18879 4.9348 5.26379 5.16771 >> >> Left argument is the radius of the "n-sphere". >> >> Right argument is the number of dimensions. >> >> I put "n-volume" in quotes, because if the dimension is 2 (for >> example), the "n-volume" is what we call the area of the circle. (And >> if the dimension is 1 that "n-volume" is the length of a line >> segment). >> >> Anyways, I stumbled across this and thought it might be interesting >> for someone else. >> >> Thanks, >> >> -- >> Raul >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
