What is the name of the type of curve traced by a point on a rolling wheel?
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 Singular point of a curve In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied. Algebraic curves in the plane may be defined as the set of points ("x", "y") satisfying an equation of the form "f"("x", "y")=0, where "f" is a polynomial function "f":R→R. If "f" is expanded as If the origin (0, 0) is on the curve then "a"=0. If "b"≠0 then the implicit function theorem guarantees there is a