Folium

The word ``folium'' means leaf-shaped. The polar equation is

$$r=\cos\theta(4a\sin^2\theta-b).$$

If $b\geq 4a$, it is a single folium. If $b=0$, it is a Bifolium. If $0<b<4a$, it is a Trifolium. The simple folium is the Pedal Curve of the Deltoid where the Pedal Point is one of the Cusps.

See also Bifolium, Folium of Descartes, Kepler's Folium, Quadrifolium, Rose, Trifolium

References

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

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