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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