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From: wws@whuxlm.UUCP (Stoll W William)
Newsgroups: net.puzzle
Subject: Re: manholes
Message-ID: <712@whuxlm.UUCP>
Date: Sun, 17-Mar-85 15:13:51 EST
Article-I.D.: whuxlm.712
Posted: Sun Mar 17 15:13:51 1985
Date-Received: Mon, 18-Mar-85 02:16:59 EST
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> 
> Mathematicians know better.  They call such curves "curves of constant
> breadth," and there are an infinity of them.  Martin Gardner did a column
> on them once.
> 
> The simplest example (besides a circle) is constructed thus: let ABC be
> an equilateral triangle.  Draw arcs AB with C as center, AC with B as center,
> BC with A as center.  The three arcs form a curve of constant breadth.
> -- 
> Col. G. L. Sicherman
> ...{rocksvax|decvax}!sunybcs!colonel

Now I understand.  Triangular manhole covers are not really triangular.
They have three vertices, but the sides are arcs, not straight lines.
Is this figure called "triangular curve of constant breadth" or is
there a shorter name?

An odd number of vertices is required when this trick is used (e.g.,
doesn't work for squares), and the polygon must be equilateral.
Arcs must be drawn using all vertices as centers.
When choosing the endpoints of the arc, always choose the two endpoints
farthest from the current center.

Bill Stoll, ..!whuxlm!wws