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 according to the solutions of "c"+"2mc"+"mc"=0. If "c"+"2mc"+"mc"=0 has two real solutions for "m", that is if "c""c"−"c"<0, then the origin is called a crunode. The curve in this case crosses itself at the origin and has two distinct tangents corresponding to the two solutions of "c"+"2mc"+"mc"=0. The function "f" has a saddle point at the origin in this case. If "c"+"2mc"+"m""c"=0 has no real solutions for "m", that is if "c""c"−"c">0, then the origin is called an acnode. In the real plane the origin is an isolated point on the curve; however when considered as a complex curve the