ENTRY CURVES Authors: Oliver Knill, Andrew Chi, 2003 Literature: www.mathworld.com, www.2dcurves.com +------------------------------------------------------------ | astroid +------------------------------------------------------------ An astroid is the curve t mapsto (cos^3(t),a sin^3(t)) with a>0. An asteroid is a 4-cusped hypocycloid. It is sometimes also called a tetracuspid, cubocycloid, or paracycle. +------------------------------------------------------------ | Archimedes spiral +------------------------------------------------------------ An Archimedes spiral is a curve described as the polar graph r(t) = a t where a>0 is a constant. In words: the distance r(t) to the origin grows linearly with the angle. +------------------------------------------------------------ | bowditch curve +------------------------------------------------------------ The bowditch curve is a special Lissajous curve r(t)=( a sin(nt+c), b sin(t)). +------------------------------------------------------------ | brachistochone +------------------------------------------------------------ A brachistochone is a curve along which a particle will slide in the shortest time from one point to an other. It is a cycloid. +------------------------------------------------------------ | Cassini ovals +------------------------------------------------------------ Cassini ovals are curves described by ((x+a) +y^2)((x-a)^2+y^2) = k^4, where k^2