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Bifolium

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

A Folium with $b=0$. 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}

See also Folium, Quadrifolium, Trifolium


References

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

MacTutor History of Mathematics Archive. ``Double Folium.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Double.html.




© 1996-9 Eric W. Weisstein
1999-05-26