Bifolium Explained

A bifolium is a quartic plane curve with equation in Cartesian coordinates:

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

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.^[1]

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

Notes and References

1. Web site: Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers. Kokoska. Stephen. 6 January 2018.