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Why are Manholes Round?


Date: 8/20/95
From: Anonymous
Subject: Man hole

My daughter and I have spent an entire day trying to locate the answer 
to the following question. The public librarian could not help us 
locate the answer.

Why is a manhole round?

We think it has something to do with physics.

Thank you.


Date: 8/26/95 at 17:3:59
From: Dr. Ken
Subject: Re: Man hole

Hello there!

I'd say it has more to do with Geometry than Physics. It's because a 
circle is the only shape that won't fall through its own hole. For 
instance, if it were a square, you could drop it through diagonally, 
because the diagonal "diameter" of a square is longer than the "diameter" 
striaght across. For any polygon, there will be "diameters" of different 
lengths, allowing you to turn the cover so that the shortest diameter 
of the cover lines up with the longest diameter of the hole, and it 
could fall through.

Dr. Ken, The Math Forum
-Check out our web site  http://mathforum.org/dr.math/   


Date: Sat, 7 Jun 1997 
From: Robert Vaul
Subject: Round Manhole Covers

Physics is a partial answer; another reason is that the shape 
causes less damage compared to shapes with corners.

- Robert Vaul


Date: Sun, 8 Jun 1997
From: Dr. Math
Subject: Round Manhole Covers

Hello Robert -

Here's an article by Ivars Peterson about manhole covers and curves of 
constant widths:

  http://www.maa.org/mathland/mathland_10_21.html   

"Rolling with Reuleaux" - Ivars Peterson (MathLand)

Why is the cover of a manhole round? The usual answer is that a circular 
lid, unlike a square or hexagonal cover, won't fall through the opening. 
The circle works because it has a constant width, defined as the distance 
between a pair of parallel lines touching the curve on opposite sides. 
For a circle, the width is simply the circle's diameter. However, the 
circle isn't the only curve of constant width. There is actually an 
infinite number of such curves, any one of which could form a manhole lid... 
The simplest such curve is known as the Reuleaux triangle... It's possible 
to construct a curve of constant width not only from an equilateral 
triangle but also from any polygon with an odd number of sides....

Your observation of course is still relevant.

Dr. Sarah, The Math Forum
-Check out our web site  http://mathforum.org/dr.math/   

    
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