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 the curve passes through the origin and write "y"="mx". Then "f" can be written If "b"+"mb" is not 0 then "f"=0 has a solution of multiplicity 1 at "x"=0 and the origin is a point of single contact with line "y"="mx". If "b"+"mb"=0 then "f"=0 has a solution of multiplicity 2 or higher and the line "y"="mx", or "b"x+"b"y=0, is tangent to the curve. In this case, if "c"+2"mc"+c"m" is not 0 then the curve has a point of double contact with "y"="mx". If the coefficient of "x", "c"+2"mc"+c"m", is 0 but the coefficient of "x" is not then the