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 When parametrised by "g"("t") = ("t",0) it is nonsingular. Hence, it is technically more correct to discuss singular points of a smooth mapping rather than a singular point of a curve. The above definitions can be extended to cover "implicit curves" which are defined as the zero set "f"(0) of a smooth function, and it is not necessary just to consider algebraic varieties. The definitions can be extended to cover curves in higher dimensions. A theorem of Hassler Whitney states Any parameterized curve can also be defined as an implicit curve, and the classification of singular points of curves can