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 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