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From: bs@faron.UUCP (Robert D. Silverman)
Newsgroups: net.math
Subject: strange shapes
Message-ID: <189@faron.UUCP>
Date: Thu, 13-Dec-84 12:58:14 EST
Article-I.D.: faron.189
Posted: Thu Dec 13 12:58:14 1984
Date-Received: Sun, 16-Dec-84 04:47:26 EST
Organization: The MITRE Corp., Bedford, Ma.
Lines: 10


	To prove that a sphere is the 3-manifold of fixed area that 
holds the largest volume is trivial. It is a simple iso-perimetric
problem in the Calculus of Variations. See for example "Lectures on the
Calculus of Variations", Bolza, Oskar, Dover Press, chapter 6.

	It amounts to finding a function G(x,y, x', y') such that
the double integral over G is fixed and for which the volume integral
is maximal.