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From: leichter@lrw.com (Jerry Leichter)
Newsgroups: comp.dcom.telecom
Subject: Re: Manhole Covers
Message-ID: <59795@bu.edu.bu.edu>
Date: 26 Jun 90 16:03:03 GMT
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X-Telecom-Digest: Volume 10, Issue 460, Message 4 of 11


Norman Yarvin claims that a triangular manhole cover cannot fall
through its own hole "if it's equilateral".  As Spock said in Star
Trek: The Wrath of Kahn - he displays two-dimensional thinking.  Stand
an equilateral triangle up on one corner so that one side is
perpendicular to the ground.  Its maximum cross-section is now the
height of the triangle, which is quite a bit less than the length of
one side.  (sqrt(3)/2 times as large, about .866).  It can thus easily
be dropped through its own hole by keeping it resting along one edge
of the hole.

There ARE geometrical figures other than circles whose cross-section
is constant at all points - Scientific American's Mathematical Games
section had articles on this years ago, with speculations about
carriages with wheels of this shape.  The simplest such figure is easy
to draw: Start with an equilateral triangle.  From each corner, draw a
circular arc joining the other two corners.  The resulting "bulging"
triangle has the required property.  As a result, it cannot fall into
its own hole if used as a manhole cover.  As I recall, such covers are
actually used somewhere!

BTW, someone brought up the issue of "non-sexist" names for manhole
covers.  There was an article in the paper about this a couple of days
ago.  It seems that some city - San Diego? - has adopted new language
for the things on all official city maps and drawings - something like
"service access portal".  The change started out as a joke which
someone took seriously.

			-- Jerry


P A T R I C K   A.  T O W N S O N  (The Cheerful Iconclast)
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