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From: jfh@browngr.UUCP (John "Spike" Hughes)
Newsgroups: net.math
Subject: Re: Re: Strange Shapes
Message-ID: <1651@browngr.UUCP>
Date: Sun, 2-Dec-84 14:56:48 EST
Article-I.D.: browngr.1651
Posted: Sun Dec  2 14:56:48 1984
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David Park asks:
  Isn't the surface of maximal volume with a given finite surface areas always
a sphere?
  I expect so, but I'd like to see a proof. It's certainly true if the bounded
region is a subset of a finite ball in 3-space (I mean the conjecture about
finite area => finite volume), but I don't see any self-evident reason that
it should be true for regions extending to infinity.
   For some cogent remarks on 'obvious' statements, see 'Proofs and Refutations',
by Imre Lakatos. It's a fascinating book on deduction in mathematics...
      -jfh