Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
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