Bifolium

Construction of the Bifolium

Bifolium for a = 1.

A bifolium is a quartic plane curve drawn in a plane via equation

$(x^{2}+y^{2})^{2}=ax^{2}y.$

Construction and equations

Given a circle C through a point O, and line L tangent to the circle at point O: for each point Q on C, define the point P such that PQ is parallel to the tangent line L, and PQ = OQ. The collection of points P forms the bifolium.

In polar coordinates, the bifolium's equation is

$\rho =a\sin \theta \cos ^{2}\theta .$

For a = 1, the total included area is approximately 0.10.

External links

• Bifolium at MathWorld