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
Singular point of a curve origin is a point of inflection of the curve. If the coefficients of "x" and "x" are both 0 then the origin is called "point of undulation" of the curve. This analysis can be applied to any point on the curve by translating the coordinate axes so that the origin is at the given point. If "b" and "b" are both 0 in the above expansion, but at least one of "c", "c", "c" is not 0 then the origin is called a double point of the curve. Again putting "y"="mx", "f" can be written Double points can be classified