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From: tmk@io.ATT.COM (59481[rjb]-t.m.ko)
Newsgroups: sci.electronics,sci.math
Subject: Constant Breadth Manhole(was Re: WHat are those holes for?)
Message-ID: <745@io.ATT.COM>
Date: 21 Jul 88 14:25:14 GMT
References: <10790@oberon.USC.EDU> <327@richp1.UUCP> <303@btree.uucp> <1550@tekirl.TEK.COM> <892@wucs2.UUCP>
Reply-To: tmk@io.UUCP (59481[rjb]-t.m.ko)
Organization: AT&T, Middletown, NJ
Lines: 46

In article <892@wucs2.UUCP> jps@wucs2.UUCP (James Sterbenz) writes:
>In article <1550@tekirl.TEK.COM> jackg@tekirl.TEK.COM (Jack Gjovaag) writes:
>>In article <303@btree.uucp> rfarris@btree.UCSD.EDU (rick farris) writes:

>>>Yes, and why the heck are manholes round?

>>Round is the only shape for the cover that guarantees that the cover can't
>>fall into the hole.  What do I win?
>
>Nothing.  I suspect that any regular polygon with an ODD number of sides
>couldn't fall into the hole.  Think about trying to rotate a triangle or
>pentagon to fit!  A circular cover is just easier to manufacture
>(kinda like a polygon with an infinite number of sides :-).
>
>-- 

Regular polygon with an ODD number of sides can also fall into the hole
unless the ledge is wide enough.
Consider a regular pentagon ABCDE. Denote midpoint of CD to be M.
Note that AM is less than AC or BD, etc.

However circle is *NOT* the only shape that can't fall into the hole.
Any shape with a constant breadth (i.e. constant width when measuring in
any direction) will do the job.
Circle is an example of a constant breadth figure.
Another example is as follows:

Construct an equilateral triangle ABC. Draw arc AB with center C.
Draw arc BC with center A. Draw arc AC with center B.
The resulting figure bounded by the 3 arcs is a constant breadth figure.


In addition, such a triangular constant breadth cover can be painted yellow
to indicate the traffic direction or the flow direction of whatever
underneath. (Note: an "equilateral triangular cover" is being used
for this purpose in some places)
Also, the triangular constant breadth shape fits human better than a circle.

Do I win the "Best Manhole Design" award?

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Tsz-Mei Ko
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