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
Elliptic curve point multiplication and "Q", addition is defined as the negation of the point resulting from the intersection of the curve, "E", and the straight line defined by the points "P" and "Q", giving the point, "R". Assuming the elliptic curve, "E", is given by , this can be calculated as: Where the points "P" and "Q", are coincident (at the same coordinates), addition is similar, except that there is no well-defined straight line through "P" and "Q", so the operation is closed using limiting case, the tangent to the curve, "E", at "P" and "Q". This is calculated as above, except with: