# 1911 Encyclopædia Britannica/Cardioid

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**CARDIOID**, a curve so named by G. F. M. M. Castillon (1708-1791), on account of its heart-like form (Gr. Καρδία, heart). 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 . There is symmetry about the initial line and a cusp at the origin. The area is , *i.e.* times the area of the generating circle; the length of the curve is . (For a figure see Limaçon.)