p Ellipsoid: A 3-dimensional solid whose cross sections are ellipses.

Ellipsoid

Pronunciation: /ɪˈlɪp sɔɪd/ ?
Wire frame ellipsoid
Figure 1: Ellipsoid. Image placed in public domain. Click on the figure for a larger image.

An ellipsoid is a 3-dimensional solid. The cross sections of an ellipsoid are ellipses. The general form of an ellipsoid equation is
((x-x0)^2/a2) + ((y-y0)^2/b2) + ((z-z0)^2/c2) = 1
where (x0,y0,z0) is the center of the ellipsoid, and a, b and c are the semi-axes of the ellipsoid.

Ellipsoid Formula
FormulaDescription
V=(4/3)*pi*a*b*cVolume
S=2*(pi)*(c^2+b*squareroot(a^2-c^2)*E(?,m)+(bc^2)/(squareroot(a^2-c^2)*F*(?,m))
where ?=arccos(c\a) for an oblate ellipsoid or ?=arccos(a\c) for a prolate ellipsoid, m=(b^2-c^2)/(b^2*sin(?)^2) and E(?,m), F(?,m) are the incomplete elliptic integrals of the first and second kind.
Surface Area
Table 1

References

  1. ellipsoid. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=ellipsoid&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Yefimov, M.. A Brief Course In Analytic Geometry, pp 114,201-207. Translated by Soroka, O.. Peace Publishers. (Accessed: 2010-01-24). http://www.archive.org/stream/briefcourseinana032746mbp#page/n117/mode/1up/search/ellipsoid.
  3. Nichols, E. J.. Analytic Geometry for Colleges, Universities, and Technical Schools, pp 262-274. Leach, Shewell, & Sandborn, 1892. (Accessed: 2010-01-24). http://www.archive.org/stream/analygeomcoll00nichrich#page/n281/mode/1up/search/ellipsoid.

More Information

  • McAdams, David. Ellipse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Ellipse.

Cite this article as:


Ellipsoid. 2010-01-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/ellipsoid.html.

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2010-01-24: Added "References" (McAdams, David.)
2008-12-17: Initial version (McAdams, David.)

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