Ellipsoid

Pronunciation: /ɪˈlɪp.sɔɪd/ Explain
Wire frame ellipsoid
Figure 1: Ellipsoid.

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 Formulas
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. McAdams, David E.. All Math Words Dictionary, ellipsoid. 2nd Classroom edition 20150108-4799968. pg 69. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Yefimov, M.. A Brief Course In Analytic Geometry. pp 114,201-207. Translated by Soroka, O.. www.archive.org. Peace Publishers. Last Accessed 7/9/2018. http://www.archive.org/stream/briefcourseinana032746mbp#page/n117/mode/1up/search/ellipsoid. Buy the book
  3. Nichols, E. J.. Analytic Geometry for Colleges, Universities, and Technical Schools. pp 262-274. www.archive.org. Leach, Shewell, & Sandborn. 1892. Last Accessed 7/9/2018. http://www.archive.org/stream/analygeomcoll00nichrich#page/n281/mode/1up/search/ellipsoid. Buy the book

More Information

  • McAdams, David E.. Ellipse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. https://www.allmathwords.org/en/e/ellipse.html.

Cite this article as:

 McAdams, David E. Ellipsoid. 3/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/ellipsoid.html.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/24/2010: Added "References". (McAdams, David E.)
12/17/2008: Initial version. (McAdams, David E.)

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