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Re: 4 large dimensionsPosted by phobos on July 23, 19101 at 07:35:18: In Reply to: Re: 4 large dimensions posted by Cooper on July 22, 19101 at 16:58:49: The coordinate method is easiest to do, but here's a quick way: Look at the integral over d-dimensional space of exp(-(1/2)sum(x_i^2)). This is just pi^(d/2). Now rewrite the same integral as an integral over the d-sphere and over the radius of r^(d-1)exp(-r^2/2). With a proper substitution for r, this is a gamma function dependent upon the dimension multiplied by the d-sphere volume. Equating the two sides gives the d-sphere volume. This trick is done in Peskin and Schroeder in, I believe, chapter 7 or so. phobos
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