Cycloid Cycloid A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity, and is also the form of a curve for which the period of an object in descent on the curve does not depend on the object's starting position. The cycloid has been
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