# ellipsoid

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Related to ellipsoid: geoid, ellipsoid joint

## ellipsoid

a geometric surface, symmetrical about the three coordinate axes, whose plane sections are ellipses or circles. Standard equation: x2/a2 + y2/b2 + z2/c2 = 1, where ?a, ?b, ?c are the intercepts on the x-, y-, and z- axes
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

## ellipsoid

(i-lip -soid) A surface or solid whose plane sections are circles or ellipses. An ellipse rotated about its major or minor axis is a particular type of ellipsoid, called a prolate spheroid (major axis) or an oblate spheroid (minor axis).
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Ellipsoid

a closed central quadric surface. An ellipsoid has a center of symmetry O (see Figure 1) and three axes of symmetry, which are called the axes of the ellipsoid. The plane sections of

Figure 1

ellipsoids are ellipses; in particular, one can always find a plane section that is a circle. In a suitable coordinate system the equation of an ellipsoid has the form

## ellipsoid

[ə′lip‚sȯid]
(mathematics)
A surface whose intersection with every plane is an ellipse (or circle).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
When the uncertainty set is flat ellipsoid, the RCB with ellipsoid set [15] is described as
Ellipsoid [epsilon]([x.sub.0], P) in [R.sup.n] with center [x.sub.0] and shape matrix P is the set
The shape of the ellipsoid is determined by the three semiprincipal axes.
A sequence of states [x.sub.i], i [member of] {1, 2, ..., N} should be chosen such that for each j, the ellipsoids [[epsilon].sub.i,j], [for all]i [not equal to] N obtained are nested ([[epsilon].sub.i+1,j] [subset] [[epsilon].sub.i,j], [Q.sub.i+1,j] < [Q.sub.i,j]).
Actually the feedback controller can make the closed-loop system stable in the ellipsoid [epsilon] = {[x.sup.T.sub.k][X.sup.- 1.sub.k]([r.sub.k])[x.sub.k] [less than or equal to] 1}.
Urediniospores globose to subglobose or ellipsoid, cinnamon brown, 17-22 x 20-24 um; wall 1-1.2 um, echinulate; germ pores 3 or 4, obscure, equatorial.
After the intersection curve has been located, the portions of the curve above and below the ellipsoid's equator are projected onto the plane z = 0 to determine the relevant closed region on the equator plane.
Different numbers of runs and ellipsoid dimensions were used depending on the envelope.
A volume of 1.62 [+ o -] 0.45 mL was obtained using the exact mathematical equation (8) to determine the volume of a scalene ellipsoid. The statistical analysis showed that there were no significant differences (p>0.05) in bean volume between the pycnometric experimental value and the mean value obtained using the mathematically exact equation for scalene ellipsoids, evidencing that Trinitario cocoa beans studied in this work could be safely approximated to this geometry.
The thin section feature has been used for determination of sense of shear, the intensity of deformation, P-T condition in the shear zone and deciphering strain ellipsoid shape.
The stretch of the ellipsoid model of the RV was determined based on different combinations of varying HR, CO and, by extension, EDV, as well as the superimposed infusion rate.

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