From: Joe Keane <jgk@netcom.com>
Newsgroups: sci.math.research
Subject: Re: Volumes of hyperbolic simplices and cubes
Date: Mon, 1 Apr 1996 00:25:33 GMT
Message-ID: <jgkDp5qIL.JtB@netcom.com>

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