Ellipsoid

Pronunciation: /ɪˈlɪp.sɔɪd/ Explain

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

is the center of the ellipsoid, and a, b and c are the semi-axes of the ellipsoid.

Ellipsoid Formulas
Formula	Description
	Volume
where $?=arccos(c\a)$ for an oblate ellipsoid or $?=arccos(a\c)$ for a prolate ellipsoid, and are the incomplete elliptic integrals of the first and second kind.	Surface Area
Table 1

References

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
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
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. http://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. http://www.allmathwords.org/en/e/ellipsoid.html.

Image Credits

All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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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