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 origin is a point of inflection of the curve. If the coefficients of "x" and "x" are both 0 then the origin is called "point of undulation" of the curve. This analysis can be applied to any point on the curve by translating the coordinate axes so that the origin is at the given point. If "b" and "b" are both 0 in the above expansion, but at least one of "c", "c", "c" is not 0 then the origin is called a double point of the curve. Again putting "y"="mx", "f" can be written Double points can be classified