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Why are manhole covers round?

While talking about circles on Pi day (March 14, 2015) Chief Scientist Carl Nelson asks the question, "why are manhole covers round?" It all comes down to the idea of curves of constant width. Circles by definition have a constant width, its diameter. Other commons shapes like squares and triangles do not have a constant width and can pass through a similarly shaped opening. Circles will not fall through. Circles are not the only example of curves of constant width. In fact, there are infinitely many such shapes with a constant width. Perhaps the simplest and most well known is the Reuleaux triangle. You can construct such a triangle by sweeping out an arc from each of the vertices of an equilateral triangle that touches the other vertices. Here's an example of a Reuleaux triangle manhole cover in San Francisco. http://bit.ly/1Dl6kba