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 or on a parametrised curve, "g"("t") = ("t","t"). Both definitions give a singular point at the origin. However, a node such as that of "y"−"x"−"x" = 0 at the origin is a singularity of the curve considered as an algebraic curve, but if we parameterize it as "g"("t") = ("t"−1,"t"("t"−1)), then "g"′("t") never vanishes, and hence the node is "not" a singularity of the parameterized curve as defined above. Care needs to be taken when choosing a parameterization. For instance the straight line "y" = 0 can be parameterised by "g"("t") = ("t",0) which has a singularity at the origin.