Circular Reasoning

Mathman strikes again. Here’s a nifty picture I have borrowed from Cracked.com. The text, by Cracked user RainbowCrash, says, “Manhole covers are round so that they cannot possibly fall through their own holes. Any shape other than a circle would be able to fit through in at least one way.”

Curiously, RainbowCrash’s profile advertises, “I’m not stupid anymore!” So let’s help him out here. There are shapes, other than a circle, that meet this definition. The requirement, when generalized, is that it must be a curve of constant width.

Wolfram defines this as “Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers.” I am not a fan of this definition, but it does describe the implications quite nicely. A circle is well known for this, but so is a curvilinear triangle, formally known as a Reuleaux triangle. Not only can this shape described a manhole cover, San Franciso uses them for it!

Cover image by Tomwsulcer / Wikimedia Commons.