Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/3/84; site talcott.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!genrad!wjh12!talcott!gjk From: gjk@talcott.UUCP (Greg J Kuperberg) Newsgroups: net.math Subject: Re: Re: Strange Shapes Message-ID: <136@talcott.UUCP> Date: Wed, 28-Nov-84 00:26:39 EST Article-I.D.: talcott.136 Posted: Wed Nov 28 00:26:39 1984 Date-Received: Fri, 30-Nov-84 05:42:39 EST References: <176@ihnet.UUCP>, <177@ihnet.UUCP> <7116@watrose.UUCP> Organization: Harvard Lines: 21 > The reply about "...all points whose distance is >= 1 unit from the origin" > is not what is intended, as has been noted. However, note also that, if > you are given a surface which encloses a finite volume, then there is > an infinite volume also enclosed by that surface, which is the "outside". > Any ideas on how to define the problem so that there is no ambiguity? > My only idea is to propose a different problem: find a surface of finite > area which has both "inside" and "outside" of infinite volume -- and these > two volumes must be distinct. > My hunch is that no such surface exists...but I don't want to go hunting > for it in any case! How about this: Find a two-dimensional surface with finite surface area which separates three-dimensional space into two regions, each of which have infinite volume. --- Greg Kuperberg harvard!talcott!gjk "Eureka!" -Archimedes