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 according to the solutions of "c"+"2mc"+"mc"=0. If "c"+"2mc"+"mc"=0 has two real solutions for "m", that is if "c""c"−"c"<0, then the origin is called a crunode. The curve in this case crosses itself at the origin and has two distinct tangents corresponding to the two solutions of "c"+"2mc"+"mc"=0. The function "f" has a saddle point at the origin in this case. If "c"+"2mc"+"m""c"=0 has no real solutions for "m", that is if "c""c"−"c">0, then the origin is called an acnode. In the real plane the origin is an isolated point on the curve; however when considered as a complex curve the