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From: moews_b@h-sc1.UUCP (david moews)
Newsgroups: net.puzzle,net.math
Subject: Re: Polar Bear Problem Sequel
Message-ID: <612@h-sc1.UUCP>
Date: Mon, 21-Oct-85 14:24:53 EDT
Article-I.D.: h-sc1.612
Posted: Mon Oct 21 14:24:53 1985
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> By the way: heat causes metal to expand.  If you have a piece of metal
> with a spherical hole in it, does the hole expand, contract, or remain
> the same when the metal is heated?  What about a square hole?  I don't
> know the answer!
> 
> ...ranjit bhatnagar

     Since the piece of metal expands uniformly when it is heated,
the hole must expand.  If you use a square hole, consider the 
portion of the metal that runs along an edge of the square hole.
If this rod-shaped portion of the metal piece was heated by itself,
it would expand in length; so it must also expand in length when it
is part of the hole.  Thus, the length of the side of the hole must get
bigger and the hole expands.

   David Moews     ...harvard!h-sc1!moews_b   moews_b%h-sc1@harvard.arpa
       "The Cray-5 can execute an infinite loop in under a minute."