Cycloid 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 also the form of a curve for which the period of an object in descent on the curve does not depend on the object's starting position. The cycloid has been
Singular point of a curve smooth function "h" so that the curve has the form "y"="h"("x") near the origin. Similarly, if "b"≠0 then there is a smooth function "k" so that the curve has the form "x"="k"("y") near the origin. In either case, there is a smooth map from R to the plane which defines the curve in the neighborhood of the origin. Note that at the origin so the curve is non-singular or "regular" at the origin if at least one of the partial derivatives of "f" is non-zero. The singular points are those points on the curve where both partial derivatives vanish, Assume