What is "limacon"

Limacon \Li`ma`[,c]on"\ (l[-e]`m[.a]`s[^o]N"), n. [F. lima[,c]on, lit., a snail.] (Geom.) A curve of the fourth degree, invented by Pascal. Its polar equation is r = a cos [theta] + b.

n. (alternative form of limaçon English)

n. (context geometry English) A plane curve with polar equation $rho\; =\; a\; +\; b,sin,theta$ or $rho\; =\; a\; +\; b,cos,theta$, of which the cardioid is a special case.

In geometry, a limaçon or limacon , also known as a limaçon of Pascal, is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle with half its radius so that the smaller circle is inside the larger circle. Thus, they belong to the family of curves called centered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp.

The term derives from the French word limaçon, which refers to small snails ( Latin limax). Depending on the position of the point generating the curve, it may have inner and outer loops (giving the family its name), it may be heart-shaped, or it may be oval.

A limaçon is a bicircular rational plane algebraic curve of degree 4.