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
Power of a point "r" and "r" are their radii. The power of a point arises in the special case that one of the radii is zero. If the two circles are orthogonal, the Darboux product vanishes. If the two circles intersect, then their Darboux product is where "φ" is the angle of intersection. Laguerre defined the power of a point "P" with respect to an algebraic curve of degree "n" to be the product of the distances from the point to the intersections of a circle through the point with the curve, divided by the "n"th power of the diameter "d". Laguerre showed