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Bifolium

Quartic plane curve

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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.

In polar coordinates, the bifolium's equation is :\rho=a\sin\theta\cdot\cos^2\theta, :while (first eqn.) :\rho^{2\cdot2}=a\cdot x^2y,,,\rho^2=\pm x\cdot(ay)^{1/2}.

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

References

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

Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

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