دانشنامه ریاضی و کامپیوتر

Bifoliate

The bifoliate is the quartic curve given by the Cartesian equation

(1)

and the polar equation

(2)

for .

It has a cusp at the origin .

The area of the bifoliate is given by

			(3)
			(4)
			(5)
			(6)

(Sloane's A093954).

Its perimeter is

(7)

(Sloane's A118289). Taking as the parameter, the bifoliate has curvature and tangential angle given by

			(8)
			(9)

SEE ALSO:Bifolium, Folium, Quadrifolium, Rose, Trifolium

REFERENCES:

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.

Sloane, N. J. A. Sequences A093954 and A118289 in "The On-Line Encyclopedia of Integer Sequences."