Bicorn

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

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.

References

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