Why are Manhole Covers Round?
November 3rd, 2006 by SplineGuy
Answer: It’s because circles have a constant width. By making the manhole cover round and having it sit on top of a hole that is just slightly smaller, the cover is not able to fall into the whole. I’m sure this is not new information to most of you. However, I did learn something new as a result of a comment on the think again blog. Circles are not the only curve of constant width, it is merely the simplest.
From Wikipedia:
In geometry, a curve of constant width is a convex planar shape whose width, measured by the distance between two opposite parallel tangent lines to its boundary, is the same regardless of the direction of those two parallel lines. One defines the width of the curve in a given direction to be the perpendicular distance between the tangents perpendicular to that direction.
More generally, any compact convex planar body D has one pair of parallel supporting lines in a given direction. A supporting line is a line that intersects the boundary of D but not the interior of D. One defines the width of the body as before. If the width of D if the same in all directions, then one says that the body is of constant width and calls its boundary a curve of constant width.
Curves of constant width can be rotated between parallel line segments. To see this, simply note that one can rotate parallel line segments (supporting lines) around curves of constant width by definition. Consequently, a curve of constant width can be rotated in a square.
The circle is obviously a curve of constant width. A nontrivial example is the Reuleaux triangle. To construct this, take an equilateral triangle ABC and draw the arc BC on the circle centered at A, the arc CA on the circle centered at B, and the arc AB on the circle centered at C. The resulting figure is of constant width.
A basic result on curves of constant width is Barbier’s theorem, which asserts that the perimeter of any curve of constant width is equal to the width (diameter) multiplied by p. A simple example of this would be a circle with width (diameter) d having a perimeter of pd.
A reuleaux triangle is a curve of constant width. Opposite sides on each square are parallel supporting lines, since each touches the curve but does not intersect the interior. The fact that the square can be rotated whilst still just intersecting the boundary shows that width (separation between parallel supporting lines) is constant in all directions.
That may be true, but I still say it is because manholes are round.
I always thought it was because men are round.
[...] As parents, we try to make the road to adulthood as smooth as possible for our children. At least, that’s what Scott and I do. If we can see a pothole ahead, we try to run ahead and be sure the round pothole cover is securely in place so the child does not fall in. However, we have to be careful to allow the child to fall once in a while so they will learn how to recover. We don’t always need to prevent them from falling, but need to be there to help them get back on their feet. It’s like when an infant is learning to go back to sleep in the middle of the night. These days are behind us now, but we have spent many hours standing just out of sight of a child who is learning to go back to sleep without behind held. [...]