Bifolium

For other uses, see Bifolium (disambiguation).

Construction of the Bifolium

Bifolium for a=1.

Construction and equations

Consider the circle C through the point O, and tangent line L to the circle at point O. For each point Q on C, draw the points P such that PQ is parellel to the tangent line L and PQ = OQ. The collection of points P forms the bifolium.^[1]

The bifolium is a quartic plane curve with equation

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

In polar coordinates, its equation is

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

References

↑ Kokoska, Stephen. "Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers" (PDF).

External links

Bifolium at MathWorld

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