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 not isolated and has two imaginary tangents corresponding to the two complex solutions of "c"+"2mc"+"m""c"=0. The function "f" has a local extremum at the origin in this case. If "c"+"2mc"+"m""c"=0 has a single solution of multiplicity 2 for "m", that is if "c""c"−"c"=0, then the origin is called a cusp. The curve in this case changes direction at the origin creating a sharp point. The curve has a single tangent at the origin which may be considered as two coincident tangents. The term "node" is used to indicate either a crunode or an acnode, in other words a