Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
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