Bifolium

File:Bifolium.gif

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.{{Cite web |last=Kokoska |first=Stephen |date= |title=Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers |url=https://facstaff.bloomu.edu/skokoska/curves.pdf |access-date=6 January 2018 |website=facstaff.bloomu.edu |publisher=}}

In polar coordinates, the bifolium's equation is

:$\backslash rho=a\backslash sin\backslash theta\backslash cdot\backslash cos^2\backslash theta,$

:while (first eqn.)

:$\backslash rho^\{2\backslash cdot2\}=a\backslash cdot\; x^2y,\backslash ,\backslash ,\backslash rho^2=\backslash pm\; x\backslash cdot(ay)^\{1/2\}.$

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

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• Folium of Descartes
• Trifolium curve

{{Reflist}}

• [https://mathworld.wolfram.com/Bifolium.html Bifolium at MathWorld] by Wolfram

Category:Plane curves

Category:Algebraic curves