Bifolium

$\begin{figure}\begin{center}\BoxedEPSF{bifolium.epsf scaled 700}\end{center}\end{figure}$

A Folium with . The bifolium is the Pedal Curve of the Deltoid, where the Pedal Point is the Midpoint of one of the three curved sides. The Cartesian equation is

$\begin{displaymath} (x^2+y^2)^2=4axy^2 \end{displaymath}$

and the Polar equation is

$\begin{displaymath} r=4a\sin^2\theta\cos\theta. \end{displaymath}$

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 152-153, 1972.