In
geometry, a
limaçon (pronounced
/'l?m?s?n/), also known as a
limaçon of Pascal, is defined as a
roulette formed when a 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 Latin word limax, which means "snail". 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.
Formal research on limaçons is attributed to Étienne Pascal, father of Blaise Pascal. However investigations began earlier by the German Renaissance artist, Albrecht Dürer. Dürer's Underweysung der Messung (Instruction in Measurement) contains specific geometric methods for producing limaçons.
