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 at least one term of degree "k" is not 0 in "f", then curve is said to have a "multiple point" of order "k" or a "k-ple point". The curve will have, in general, "k" tangents at the origin though some of these tangents may be imaginary. A parameterized curve in "R" is defined as the image of a function "g":R→R, "g"("t") = ("g"("t"),"g"("t")). The singular points are those points where Many curves can be defined in either fashion, but the two definitions may not agree. For example, the cusp can be defined on an algebraic curve, "x"−"y" = 0,