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Piriform Surface

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PiriformSurface

A generalization to a quartic three-dimensional surface is the quartic surface of revolution

(x^4-ax^3)+a^2(y^2+z^2)=0,
(1)

illustrated above. With a=1, this surface is termed the "zeck" surface by Hauser. It has volume

V=1/(20)pia^3,
(2)

geometric centroid

x^_=2/3a
(3)
y^_=0
(4)
z^_=0,
(5)

and inertia tensor

I=[5/(126)Ma^2 0 0; 0 (125)/(252)Ma^2 0; 0 0 (125)/(252)Ma^2]
(6)

for constant density and mass M.

See also

Pear Curve, Piriform Curve

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References

Hauser, H. "Gallery of Singular Algebraic Surfaces: Zeck." https://homepage.univie.ac.at/herwig.hauser/gallery.html.Nordstrand, T. "Surfaces." http://jalape.no/math/surfaces.

Cite this as:

Weisstein, Eric W. "Piriform Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PiriformSurface.html

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