Cycloid Cycloid A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity, and is also the form of a curve for which the period of an object in descent on the curve does not depend on the object's starting position. The cycloid has been
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,