From: rjohnson@apple.com (Robert Johnson)
Newsgroups: sci.math
Subject: Re: Volume of a sphere
Date: 4 Feb 1995 06:51:46 -0800

In article <3gr9hh$dqc@netserver.univ-lille1.fr>,
Philippe.Preux <preux@lifl.lifl.fr> wrote:
>  What is the volume of a sphere of radius R in a D-dimensional space ?

           D/2
         pi         D
    -------------- R
    gamma(D/2 + 1)

where gamma(x + 1) = x gamma(x).  For integer D, the only values you need
to generate the rest are gamma(1/2) = sqrt(pi) and gamma(1) = 1.

For even D, this is

       D/2
     pi     D
    ------ R
    (D/2)!

For odd D this is 

     D              (D-1)/2
    2  ((D-1)/2)! pi         D
    ----------------------- R
              D!

Rob Johnson
Apple Computer, Inc.
rjohnson@apple.com