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 smooth function "h" so that the curve has the form "y"="h"("x") near the origin. Similarly, if "b"≠0 then there is a smooth function "k" so that the curve has the form "x"="k"("y") near the origin. In either case, there is a smooth map from R to the plane which defines the curve in the neighborhood of the origin. Note that at the origin so the curve is non-singular or "regular" at the origin if at least one of the partial derivatives of "f" is non-zero. The singular points are those points on the curve where both partial derivatives vanish, Assume