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Encyclopedia Britannica



CARDIOID

This article appears in Volume V05, Page 324 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: CAR-CAU
CARDIOID , a
curve
  so named by G. F. M. M. Castillon (r7o8-1791), on
account
  of its heart-like form (Gr. Kap&ia, heart). It was mathematically treated by 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
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(r+cos0). There is symmetry about the initial line and a
cusp
  at the origin. The area is fa2, i.e. 12 times the area of the generating circle; the length of the
curve
  is 8a. (For a figure see LIMACON.)


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