Roulette (curve) application of this is that a square wheel could roll without bouncing on a road that is a matched series of catenary arcs. Roulette (curve) In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, and involutes. Roughly speaking, a roulette is the curve described by a point (called the "generator" or "pole") attached to a given curve as that curve rolls without slipping, along a second given curve that is fixed. More precisely, given a curve attached to a plane which is moving so that the curve rolls, without slipping, along
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