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 according to the solutions of "c"+"2mc"+"mc"=0. If "c"+"2mc"+"mc"=0 has two real solutions for "m", that is if "c""c"−"c"<0, then the origin is called a crunode. The curve in this case crosses itself at the origin and has two distinct tangents corresponding to the two solutions of "c"+"2mc"+"mc"=0. The function "f" has a saddle point at the origin in this case. If "c"+"2mc"+"m""c"=0 has no real solutions for "m", that is if "c""c"−"c">0, then the origin is called an acnode. In the real plane the origin is an isolated point on the curve; however when considered as a complex curve the