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\begin{figure}\begin{center}\BoxedEPSF{bicorn.epsf scaled 800}\end{center}\end{figure}

The bicorn is the name of a collection of Quartic Curves studied by Sylvester in 1864 and Cayley in 1867 (MacTutor Archive). The bicorn is given by the parametric equations

$\displaystyle x$ $\textstyle =$ $\displaystyle a\sin t$  
$\displaystyle y$ $\textstyle =$ $\displaystyle {a\cos^2 t(2+\cos t)\over 3\sin^2 t}.$  

The graph is similar to that of the Cocked Hat Curve.


Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 147-149, 1972.

MacTutor History of Mathematics Archive. ``Bicorn.''

© 1996-9 Eric W. Weisstein