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 or on a parametrised curve, "g"("t") = ("t","t"). Both definitions give a singular point at the origin. However, a node such as that of "y"−"x"−"x" = 0 at the origin is a singularity of the curve considered as an algebraic curve, but if we parameterize it as "g"("t") = ("t"−1,"t"("t"−1)), then "g"′("t") never vanishes, and hence the node is "not" a singularity of the parameterized curve as defined above. Care needs to be taken when choosing a parameterization. For instance the straight line "y" = 0 can be parameterised by "g"("t") = ("t",0) which has a singularity at the origin.