Associated Topics || Dr. Math Home || Search Dr. Math

### 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

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/

```
Associated Topics:
Elementary Puzzles

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search