In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation[1]
In 1864, James Joseph Sylvester studied the curve
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 . If we move and to the origin and perform an imaginary rotation on by substituting for and for in the bicorn curve, we obtain
The parametric equations of a bicorn curve are