last updated: 2004-09-04


cocked-hatThe bicorn curve has two (bi) horns (corn), an alternative name is derived from its resemblance to a military hat: cocked-hat 1).



The bicorn can be constructed as follows.
Let there be two tangent circles C1 and C2 of equal size.
Let Q be a point on C1, and R its projection on the y-axis.
Let m be the polar inverse (a line) of C1 with respect to Q.
Then the bicorn is formed by the points P which are the intersection of m and QR.

Sylvester (1864) was the first to investigate the curve, followed by Cayley in 1867 and Longchamps in 1897.



1) In German: Zweihorn.
In Italian: bicorno or feluca.