Roulette (curve) application of this is that a square wheel could roll without bouncing on a road that is a matched series of catenary arcs. Roulette (curve) In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, and involutes. Roughly speaking, a roulette is the curve described by a point (called the "generator" or "pole") attached to a given curve as that curve rolls without slipping, along a second given curve that is fixed. More precisely, given a curve attached to a plane which is moving so that the curve rolls, without slipping, along
Square wheel Square wheel A square wheel is a wheel that, instead of being circular, has the shape of a square. While literal square wheels exist, a more common use is as a metaphor meaning feeling bad and naive (see reinventing the wheel). A square wheel can roll smoothly if the ground consists of evenly shaped inverted catenaries of the right size and curvature. A different type of square-wheeled vehicle was invented in 2006 by Jason Winckler of Global Composites, Inc. in the United States. This has square wheels, linked together and offset by 22.5°, rolling on a flat surface. The prototype