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
Singular point of a curve double point which is not a cusp. The number of nodes and the number of cusps on a curve are two of the invariants used in the Plücker formulas. If one of the solutions of "c"+"2mc"+"mc"=0 is also a solution of "d"+"3md"+"3m""d"+"m""d"=0 then the corresponding branch of the curve has a point of inflection at the origin. In this case the origin is called a "flecnode". If both tangents have this property, so "c"+"2mc"+"mc" is a factor of "d"+"3md"+"3m""d"+"m""d", then the origin is called a "biflecnode". In general, if all the terms of degree less than "k" are 0, and