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 the curve passes through the origin and write "y"="mx". Then "f" can be written If "b"+"mb" is not 0 then "f"=0 has a solution of multiplicity 1 at "x"=0 and the origin is a point of single contact with line "y"="mx". If "b"+"mb"=0 then "f"=0 has a solution of multiplicity 2 or higher and the line "y"="mx", or "b"x+"b"y=0, is tangent to the curve. In this case, if "c"+2"mc"+c"m" is not 0 then the curve has a point of double contact with "y"="mx". If the coefficient of "x", "c"+2"mc"+c"m", is 0 but the coefficient of "x" is not then the