General:Roulette (curve): In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, and involutes. Roughly speaking, it is the curve described by a point (called the generator or pole) attached to a given curve as it rolls without slipping along a second given curve.
Really big picture:Differential geometry of curves: Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.
Epicycloid: In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called epicycle — which rolls without slipping around a fixed circle. It is a particular kind of roulette.
Hypocycloid: In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle.
Epitrochoid: An epitrochoid is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle.
Hypotrochoid: A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.
Involute: In the differential geometry of curves, an involute of a smooth curve is another curve, obtained by attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound.
Rose (mathematics): In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates.
Quadrifolium: The quadrifolium is a type of rose curve with n=2.
