Trifolium

Lawrence (1972) defines a trifolium as a Folium with $b\in (0,4a)$. However, the term ``the'' trifolium is sometimes applied to the Folium with $b=a$, which is then the 3-petalled Rose with Cartesian equation

$$(x^2+y^2)[y^2+x(x+a)]=4axy^2$$

and polar equation

$$r=a\cos\theta(4\sin^2\theta-1)=-a\cos(3\theta).$$

The trifolium with $b=a$ is the Radial Curve of the Deltoid.

See also Bifolium, Folium, Quadrifolium

References

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

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