CARDIOID

cardioid, a curve so named by g.f.m.m. castillon (1708-1791), on account of its heart-like form (gr. [greek: kardia], 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(1 + cos [theta]). there is symmetry about the initial line and a cusp at the origin. the area is {3/2}[pi]a^2, i.e. 1-1/2 times the area of the generating circle; the length of the curve is 8a. (for a figure see limacon.) cardona (perhaps the anc. _udura_), a town of north-eastern spain, in the province of barcelona; about 55 m. n.w. of barcelona, on a hill almost surrounded by the river cardoner, a branch of the llobregat. pop. (1900) 3855. cardona is a picturesque and old-fashioned town, with moorish walls and citadel, and a 14th-century church. it is celebrated for the extensive deposit of rock salt in its vicinity. the salt forms a mountain mass about 300 ft. high and 3 m. in circumference, covered by a thick bed of a reddish-brown clay, and apparently resting on a yellowish-grey sandstone. it is generally more or less translucent, and large masses of it are quite transparent. the hill is worked like a mine; pieces cut from it are carved by artists in cardona into images, crucifixes and many articles of an ornamental kind.