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From: uafhcx!cdc@uafhp.uark.edu (C. D. Covington)
Newsgroups: comp.dcom.telecom
Subject: Re: Manhole Covers
Message-ID: <59792@bu.edu.bu.edu>
Date: 27 Jun 90 14:53:43 GMT
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X-Telecom-Digest: Volume 10, Issue 460, Message 2 of 11


In article <9276@accuvax.nwu.edu>, yarvin-norman@cs.yale.edu (Norman
Yarvin) writes:
 
> rees@dabo.ifs.umich.edu (Jim Rees) writes:

> >>Has anyone ever noticed non-round manhole covers?  Nashua and Hudson,
> >>N.H.  have TRIANGULAR ones - don't know what service or utility.

> >I think this has been discussed before.  Round covers are popular
> >because it's impossible for the cover to fall into the hole.

> This also holds for triangular covers.  (only if they are equilateral,
> though.)

    I can't keep from jumping in on this last comment.  I don't
believe this to be true.  The property of round covers that keeps them
from falling through is that of constant width.  There exist an entire
family of possible closed curves of constant width, the most obvious
being a perfect circle.  An equilateral triangle is not one of them.
 
    On the other hand, if you take the vertices of the equilateral
triangle and use a compass to construct three arcs, each passing
through two vertices and using the other vertex as a center point,
then an alternative curve of constant width results.  That is, if the
points A, B, and C are equidistant from each other.  The place the
compass point on A and draw an arc from B to C, and repeat this
process with the point on B and then C, drawing arcs to the remaining
points.

    A manhole cover constructed in this way will not fall through.
Try it by cutting this shape out of a piece of cardboard and dropping
it against the hole you made cutting it out.  It works!


C. David Covington (WA5TGF)  cdc@uafhcx.uark.edu     (501) 575-6583
Asst Prof, Elec Eng          Univ of Arkansas        Fayetteville, AR 72701

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