User:Kithburd/Notes

Organizing/interlinking this set of similar mathematics articles:

 * 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.


 * Tangentially, Lissajous curve?


 * Cycloid: A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line.

Applications:

 * Spirograph


 * Deferent and epicycle