Pear-Shaped Curve
PearShapedCurve
A curve given by the Cartesian equation
| b^2y^2=x^3(a-x). |
(1)
|
It has area
| [画像: A=(a^3pi)/(8b). ] |
(2)
|
The curvature is
![画像: kappa(x)=(2b^2(3a^2-12ax+8x^2))/(sqrt(x)[4b^2(a-x)+(3a-4x)^2x]).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Pear-ShapedCurve/NumberedEquation3.svg){kind=link}
See also
Pear Curve, Piriform Curve, Teardrop CurveExplore with Wolfram|Alpha
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References
MacTutor History of Mathematics Archive. "Pear-Shaped Cubic." https://mathshistory.st-andrews.ac.uk/Curves/Pearshaped/.Referenced on Wolfram|Alpha
Pear-Shaped CurveCite this as:
Weisstein, Eric W. "Pear-Shaped Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Pear-ShapedCurve.html