Does anything seem wrong with the picture at right? Although seemingly impossible, the combination of square wheels riding on a roadway comprised of “inverted catenaries” results in a perfectly smooth ride. In fact, for almost any shape, a corresponding surface can be designed to produce a smooth ride:
As the number of a polygon’s sides increases, these catenary segments get shorter and flatter. Ultimately, for an infinite number of sides (in effect, a circle), the curve becomes a straight, horizontal line.
So, what are the benefits of this epiphany? None that I can see, but it is pretty interesting…
