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
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