From:Joe Keane <jgk@netcom.com>Date:Mon, 1 Apr 1996 00:25:33 GMTNewsgroups:sci.math.researchSubject:Re: Volumes of hyperbolic simplices and cubes

It seems like this sort of thing should be known, any good references? I found a good approach for computing the volume of the ideal hypercube. I have some ideas for the simplex case, but it needs more work. Here's an asymptotic formula for the volume of the cube: C(n) ~ A * B^n / Gamma(1/2*(n+1)) A = 2*sqrt(pi) ~= 3.545 B ~= 1.0820884492703634 Here are some numerical results: n C(n) -- ---------- 2 6.28318531 3 5.07470803 4 3.92259368 5 2.75861972 6 1.77509205 7 1.05622467 8 0.58671298 9 0.30663832 10 0.15174916 11 0.07148221 12 0.03219072 13 0.01390962 14 0.00578505 15 0.00232207 16 0.00090164 -- Joe Keane, amateur mathematician