CARDIOID  , a See also:

• CURVE (Lat. curvus, bent)

curve so named by G . F . M . M . Castillon (r7o8-1791), on See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of its See also:

• HEART
• HEART, LUNG

heart-like See also:

• FORM (Lat. forma)

form (Gr . Kap&ia, heart) . It was mathematically treated by See also:

• LOUIS
• LOUIS (804–876)
• LOUIS (893–911)
• LOUIS, JOSEPH DOMINIQUE, BARON (1755-1837)
• LOUIS, or LEWIS (from the Frankish Chlodowich, Chlodwig, Latinized as Chlodowius, Lodhuwicus, Lodhuvicus, whence-in the Strassburg oath of 842-0. Fr. Lodhuwigs, then Chlovis, Loys and later Louis, whence Span. Luiz and—through the Angevin kings—Hungarian

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

epicycloid in which the See also:

• ROLLING

rolling and fixed circles are equal in See also:

• DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter, as the inverse of a See also:

• PARABOLA

parabola for its See also:

• FOCUS (Latin for " hearth " or " fireplace ")

focus, or as the See also:

• CAUSTIC (Gr. rcavvraubs, burning)

caustic produced by the reflection at a spherical See also:

• SURFACE

surface of rays emanating from a point on the circumference . The polar See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation to the cardioid is r=a(r+cos0) . There is symmetry about the initial See also:

• LINE

line and a See also:

• CUSP (Lat. cuspis, a spear, point)

cusp at the origin . The See also:

• AREA

area is fa2, i.e .

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