What is the area of a Bicycle Crescent? A bicyclist rides through a long, shallow puddle of water.

Then he makes a right-angle turn onto a side street. The rear wheel takes a shortcut, in a futile attempt to catch up with the front wheel. The wet wheels make a crescent shape on the pavement. It turns out that the area of the crescent is path-independent. In other words, the area is the same, whether the bicycle makes a sharp turn or a gradual turn. If the distance between the two axles is d, what is the area of the crescent?

A friend of mine was the first person to solve this problem. Standard integral calculus is absolutely useless here.