Piriform Surface
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)
|
x^_ = 2/3a
(3)
y^_ =
(4)
z^_ = 0,
(5)
and inertia tensor
![画像: I=[5/(126)Ma^2 0 0; 0 (125)/(252)Ma^2 0; 0 0 (125)/(252)Ma^2]](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/PiriformSurface/NumberedEquation3.svg){kind=link}
for constant density and mass M.
See also
Pear Curve, Piriform CurveExplore with Wolfram|Alpha
WolframAlpha
More things to try:
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.htm.Referenced on Wolfram|Alpha
Piriform SurfaceCite this as:
Weisstein, Eric W. "Piriform Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PiriformSurface.html