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 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,