The mathematician Stan Wagon has created a bicycle with square wheels. It doesn’t work on flat land, of course — but it rides perfectly when you roll along a road made of of “catenaries”. And what the heck is a catenary? Glad you asked! As a story about the bicycle notes:

A catenary is the curve describing a rope or chain hanging loosely between two supports. At first glance, it looks like a parabola. In fact, it corresponds to the graph of a function called the hyperbolic cosine. Turning the curve upside down gives you an inverted catenary—just like each bump of Wagon’s road.

The thing is, you can create a catenary curve by spinning a square on its axis and tracing the trajectory of a point. That’s a little hard to visualize, but if you go to that page, there’s a cool animation showing how it works.