A quartic algebraic curve also called the pegtop curve and given by the Cartesian
equation

(1)

and the parametric curves
for .
It was studied by G. de Longchamps in 1886.
The area of the piriform is

(4)

which is exactly the same as the ellipse with semiaxes and .
The curvature of the piriform is given by

(5)

See also
Butterfly Curve,
Dumbbell Curve,
Eight Curve,
Heart
Surface,
Pear Curve,
Piriform
Surface
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References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 71, 1989.Lawrence,
J. D. A
Catalog of Special Plane Curves. New York: Dover, pp. 148150, 1972.
Cite this as:
Weisstein, Eric W. "Piriform Curve." From
MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/PiriformCurve.html
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