# Cardioid

**CARDIOID**, a curve so named by G.F.M.M. Castillon (1708-1791), on account of its heart-like form . It was mathematically treated by Louis
Carré in 1705 and Koersma in 1741. It is a particular form of the limaçon (*q.v.*) and is generated in the same way. It may be regarded as an
epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the
reflection at a spherical surface of rays emanating from a point on the circumference. The polar equation to the cardioid is r = a(1 + cos θ). There is
symmetry about the initial line and a cusp at the origin. The area is 3/2πa, *i.e.* 1
times the area of the generating circle; the length of the curve is 8a. (For a figure see Limaçon.)

*Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)*