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CARDIOID

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Originally appearing in Volume V05, Page 324 of the 1911 Encyclopedia Britannica.
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CARDIOID , a See also:

curve so named by G. F. M. M. Castillon (r7o8-1791), on See also:account of its See also:heart-like See also:form (Gr. Kap&ia, heart). It was mathematically treated by See also:Louis Carre in 1705 and Koersma in 1741. It is a particular form of the limacon (q.v.) and is generated in the same way. It may be regarded as an See also:epicycloid in which the See also:rolling and fixed circles are equal in See also:diameter, as the inverse of a See also:parabola for its See also:focus, or as the See also:caustic produced by the reflection at a spherical See also:surface of rays emanating from a point on the circumference. The polar See also:equation to the cardioid is r=a(r+cos0). There is symmetry about the initial See also:line and a See also:cusp at the origin. The See also:area is fa2, i.e.

12 times the area of the generating circle; the length of the curve is 8a.

End of Article: CARDIOID

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