Bifolium

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

(x^{2} + y^{2})^{2} = a x^{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

ρ = a \sin θ \cdot \cos^{2} θ,

while (first eqn.)

ρ^{2 \cdot 2} = a \cdot x^{2} y, ρ^{2} = \pm x \cdot (a y)^{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" (PDF). facstaff.bloomu.edu. Retrieved 6 January 2018.

External links

Bifolium at MathWorld by Wolfram

[1] Kokoska, Stephen. "Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers" (PDF). facstaff.bloomu.edu. Retrieved 6 January 2018.

Bifolium

Construction and equations

See also

References

External links