AskDefine | Define bicorn

Dictionary Definition

bicorn adj : having two horns or horn-shaped parts; "a bicornuate uterus" [syn: bicorned, bicornate, bicornuate, bicornuous] n : a cocked hat with the brim turned up to form two points [syn: bicorne]

Extensive Definition

The bicorn is also known as a cocked hat curve, due to its resemblance to a bicorne. It is a curve with equation
y^2(a^2-x^2)=(x^2+2ay-a^2)^2 \,
with two cusps, symmetrical around the y-axis.
The bicorn is a plane algebraic curve of degree four and genus zero. It has two cusp singularities in the real plane, and a double point in the complex projective plane at x=0, z=0 . If we move x=0 and z=0 to the origin substituting and perform an imaginary rotation on x bu substituting ix/z for x and 1/z for y in the bicorn curve, we obtain
(x^2-2az+a^2z^2)^2 = x^2+a^2z^2.\,
This curve, a limaçon, has an ordinary double point at the origin, and two nodes in the complex plane, at x = ± i and z=1.
bicorn in Slovak: Bicorn

Synonyms, Antonyms and Related Words

Cynthian, S-shaped, corniform, crescent, crescent-shaped, crescentic, crescentiform, crescentlike, falcate, falciform, horn-shaped, horned, lunar, lunate, luniform, lunular, menisciform, meniscoid, moon-shaped, moonlike, semicircular, semilunar, sickle-like, sickle-shaped, sigmoid, two-horned
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