Cycloid plates of golden age violins are closely modeled by curtate cycloid curves. Later work indicates that curtate cycloids do not serve as general models for these curves, which vary considerably. 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
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