Piriform Curve
Piriform
A quartic algebraic curve also called the peg-top curve and given by the Cartesian equation
| a^4y^2=b^2x^3(2a-x) |
(1)
|
and the parametric curves
x = a(1+sint)
(2)
y = bcost(1+sint)
(3)
for t in [0,2pi). It was studied by G. de Longchamps in 1886.
The area of the piriform is
| A=piab, |
(4)
|
which is exactly the same as the ellipse with semiaxes a and b.
The curvature of the piriform is given by
![画像: kappa(t)=-(ab[2+3sint+sin(3t)])/(2{a^2cos^2t+b^2[cos(2t)-sint]^2}^(3/2)).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/PiriformCurve/NumberedEquation3.svg){kind=link}
See also
Butterfly Curve, Dumbbell Curve, Eight Curve, Heart Surface, Pear Curve, Piriform SurfaceExplore with Wolfram|Alpha
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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. 148-150, 1972.Referenced on Wolfram|Alpha
Piriform CurveCite this as:
Weisstein, Eric W. "Piriform Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PiriformCurve.html