| by Flemming Funch|
From Roland Piquepaille's Technology Trends. So, you didn't think a bicycle could have square wheels? Well, it all depends on the surface you're riding on.
Stan Wagon, a mathematician at Macalester College in St. Paul, Minn., has a bicycle with square wheels. It's a weird contraption, but he can ride it perfectly smoothly. His secret is the shape of the road over which the wheels roll.
OK, so here's an idea: What about wheels that dynamically change shape quickly enough that they always fit whatever road surface you're going over, so that you can always have a smooth ride. And we might become less attached to smooth surfaces.
A square wheel can roll smoothly, keeping the axle moving in a straight line and at a constant velocity, if it travels over evenly spaced bumps of just the right shape. This special shape is called an inverted catenary.
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.