# ellipsoid

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## 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

## 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).

## 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).
References in periodicals archive ?
Whereas these coordinates have been described as prolate spheroidal, the presence of a characteristic ellipsoid with its two foci makes preferable a description as ellipsoidal coordinates.
The slope is cut by these ellipsoids, and the safety factor of these ellipsoidal slip surfaces can be computed, where the minimum one is the critical slip surface.
2](x) correspond to closed regions on the equator planes for the two quadrics (that is, the plane z = 0 for the ellipsoid and the plane z = l for the sphere).
The potential in space of this homogeneous ellipsoid is given by
Using high resolution FDTD simulation, we have considered the basic characteristics (effective length, peak intensity, and FWHM) of nanojets formed in the vicinity of dielectric core-shell ellipsoids with different types of index grading.
However, a fiber can be approximated by a prolate ellipsoid for which the polarizability can be solved analytically.
With the surfactant lowering the drop's surface tension, ellipsoid particles did not get stuck at the interface and flowed freely to the edge.
In previous studies, we considered the measurement errors in RECIST based on measurements of physical ellipsoids (2) and randomly-oriented single ellipsoids treated theoretically (3).
On histological examination of the 1 hour post carbon injected spleen, it already contained some carbon-laden cells around the ellipsoids scattered within the red pulp (Fig.
In order to compare the efficiency of the proposed method with the robust quadratic control, the volumes of stable reflection vector polytopes and stable ellipsoids derived via optimization over linear matrix inequalities (LMIs)  are calculated.

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