## Piriform

A plane curve also called the Peg Top and given by the Cartesian equation

 (1)

and the parametric curves
 (2) (3)

for . It was studied by G. de Longchamps in 1886. The generalization to a Quartic 3-D surface
 (4)

is shown below (Nordstrand).

See also Butterfly Curve, Dumbbell Curve, Eight Curve, Heart Surface, Pear Curve

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. 148-150, 1972.

Nordstrand, T. Surfaces.'' http://www.uib.no/people/nfytn/surfaces.htm.