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 not isolated and has two imaginary tangents corresponding to the two complex solutions of "c"+"2mc"+"m""c"=0. The function "f" has a local extremum at the origin in this case. If "c"+"2mc"+"m""c"=0 has a single solution of multiplicity 2 for "m", that is if "c""c"−"c"=0, then the origin is called a cusp. The curve in this case changes direction at the origin creating a sharp point. The curve has a single tangent at the origin which may be considered as two coincident tangents. The term "node" is used to indicate either a crunode or an acnode, in other words a