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
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: