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
Deltoid curve line segment can slide with each end on the deltoid and remain tangent to the deltoid. The point of tangency travels around the deltoid twice while each end travels around it once. The dual curve of the deltoid is which has a double point at the origin which can be made visible for plotting by an imaginary rotation y ↦ iy, giving the curve with a double point at the origin of the real plane. The area of the deltoid is formula_9 where again "a" is the radius of the rolling circle; thus the area of the deltoid is twice