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
Aristotle's wheel paradox else has been able to discover whether the smaller circle touches the same point twice, or proceeds by leaps and sliding.In his "Two New Sciences", Galileo uses the problem of the wheel to argue for a certain kind of atomism. Galileo begins his analysis by considering a pair of concentric hexagons, as opposed to a pair of circles. Imagining this hexagonal wheel "rolling" on a surface, Galileo notices that the inner hexagon "jumps" a little space, with each roll of the outer hexagon onto a new face. He then imagines what would happens in the limit as the number faces