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From: bundy@oasys.UUCP
Newsgroups: net.math
Subject: Largest 2-d object around 90-degree corner?
Message-ID: <167@oasys.UUCP>
Date: Wed, 11-Dec-85 16:52:05 EST
Article-I.D.: oasys.167
Posted: Wed Dec 11 16:52:05 1985
Date-Received: Sat, 14-Dec-85 08:15:40 EST
Distribution: net
Organization: NBI,Inc, Boulder CO
Lines: 32


We all remember the old first semester calculus question asking what
is the longest board (i.e. 1-dimensional rigid body) that can fit
around a 90 degree turn between two corridors.  What is the biggest
two dimensional rigid body that can fit around the turn and can also
slide freely down both corridors:

______________________________
                             I
                             I
                             I
_________________            I
                 I           I
                 I           I
                 I           I
                 I           I
                 I           I
                 I           I
                 I           I
                 I           I
   

Both corridors are infinite length, width a, and we are interested in
the 2-d rigid body of greatest area that goes around the corner.  
Certainly the square of width a fits, but a little thought will reveal
shapes of significantly greater area.

-- 


Bruce Bundy

{ucbvax,hao,allegra}!nbires!oasys!bundy