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Pear-Shaped Curve


PearShapedCurve

A curve given by the Cartesian equation

 b^2y^2=x^3(a-x).
(1)

It has area

 A=(a^3pi)/(8b).
(2)

The curvature is

 kappa(x)=(2b^2(3a^2-12ax+8x^2))/(sqrt(x)[4b^2(a-x)+(3a-4x)^2x]).
(3)

See also

Pear Curve, Piriform Curve, Teardrop Curve

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References

MacTutor History of Mathematics Archive. "Pear-Shaped Cubic." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Pearshaped.html.

Cite this as:

Weisstein, Eric W. "Pear-Shaped Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Pear-ShapedCurve.html

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