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From: halle@hou2b.UUCP (J.HALLE)
Newsgroups: net.puzzle,net.math
Subject: Re: Polar Bear Problem Sequel
Message-ID: <636@hou2b.UUCP>
Date: Tue, 22-Oct-85 08:45:36 EDT
Article-I.D.: hou2b.636
Posted: Tue Oct 22 08:45:36 1985
Date-Received: Wed, 23-Oct-85 05:44:32 EDT
References: <7458@watdaisy.UUCP>
Organization: AT&T Bell Labs, Holmdel NJ
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Xref: watmath net.puzzle:1062 net.math:2410

>> 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

>Physically speaking, it beats me, too, but coopers bind their barrels by
>heating a metal ring, placing it over the barrel pieces, and then cooling the
>ring.  This would mean that the hole would expand when the metal is heated.
>This looks like a job for second year calculus students.
>
>David Tanguay

This looks like a job for a first semester high school physics student.
As you heat the metal, it expands in all dimensions.  It stays exactly
congruent (assuming uniform heating).  Thus the hole expands, a spherical
bubble inside expands, a square hole stays square, etc.