Ride on a square-wheeled tricycle. Why is the ride so smooth?

Each hump in the roadway is actually a special curve called a "catenary." A catenary is the curve made by a hanging rope or chain, just like the ones that surround the exhibit. On this roadway, the catenaries are upside down. Mathematical analysis can be used to figure out that this shape allows square wheels to roll smoothly. For many kinds of oddly shaped wheels, there is a compensating road. Why do you think the wheels are all different sizes?