Has the n-sphere become concave in higher dimension? Вт, 15 авг 2017, Jimmy Gauvin написал(а): > Funny how the n-Sphere volume dwindles for the higher dimensions. > Not quite intuitive but the factorial always "win" even with bigger radii. > > The hypercubes do not share this characteristic (V= edge ^ n) > > > > On Tue, Aug 15, 2017 at 3:33 PM, Ben Gorte - CITG <b.g.h.go...@tudelft.nl> > wrote: > > > A little surprise (to me) was > > plot 1 sphvol i.30 > > (for example) > > > > Can you predict it? > > > > greetings, > > Ben > > ________________________________________ > > From: Programming [programming-boun...@forums.jsoftware.com] on behalf of > > Raul Miller [rauldmil...@gmail.com] > > Sent: Tuesday, August 15, 2017 19:55 > > To: Programming forum > > Subject: [Jprogramming] "n-volume" of an "n-sphere" > > > > 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
-- regards, ==================================================== GPG key 1024D/4434BAB3 2008-08-24 gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3 gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
