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 at least one term of degree "k" is not 0 in "f", then curve is said to have a "multiple point" of order "k" or a "k-ple point". The curve will have, in general, "k" tangents at the origin though some of these tangents may be imaginary. A parameterized curve in "R" is defined as the image of a function "g":R→R, "g"("t") = ("g"("t"),"g"("t")). The singular points are those points where Many curves can be defined in either fashion, but the two definitions may not agree. For example, the cusp can be defined on an algebraic curve, "x"−"y" = 0,