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 origin is not isolated and has two imaginary tangents corresponding to the two complex solutions of "c"+"2mc"+"m""c"=0. The function "f" has a local extremum at the origin in this case. If "c"+"2mc"+"m""c"=0 has a single solution of multiplicity 2 for "m", that is if "c""c"−"c"=0, then the origin is called a cusp. The curve in this case changes direction at the origin creating a sharp point. The curve has a single tangent at the origin which may be considered as two coincident tangents. The term "node" is used to indicate either a crunode or an acnode, in other words a