is also known as a cocked hat curve
, due to its resemblance to a bicorne
. It is a curve
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
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.