Online Encyclopedia

CARDIOID

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

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curve so named by G . F . M . M . Castillon (r7o8-1791), on
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account of its
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heart-like
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form (Gr . Kap&ia, heart) . It was mathematically treated by
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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
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epicycloid in which the
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rolling and fixed circles are equal in
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diameter, as the inverse of a
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parabola for its
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focus, or as the
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caustic produced by the reflection at a spherical
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surface of rays emanating from a point on the circumference . The polar
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equation to the cardioid is r=a(r+cos0) . There is symmetry about the initial
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line and a
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cusp at the origin . The
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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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CARDING 		[next]
CARDONA (perhaps the anc. Udura)

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