Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!genrad!wjh12!foxvax1!brunix!browngr!jfh 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 Date-Received: Thu, 6-Dec-84 06:12:16 EST References: ubu.341, <176@ihnet.UUCP>, <177@ihnet.UUCP> <7116@watrose.UUCP> <136@talcott.UUC Lines: 10 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