# ellipsoid

## Definitions

• WordNet 3.6
• adj ellipsoid having the nature or shape of an ellipsoid
• n ellipsoid a surface whose plane sections are all ellipses or circles "the Earth is an ellipsoid"
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Webster's Revised Unabridged Dictionary
• Interesting fact: The earth is not perfectly round. Technically, it's a triaxial ellipsoid, which is to say that it's nearly spherical, but flattened at the top and bottom.
• n Ellipsoid (Geom) A solid, all plane sections of which are ellipses or circles. See Conoid n., 2 .☞ The ellipsoid has three principal plane sections, a b, and c, each at right angles to the other two, and each dividing the solid into two equal and symmetrical parts. The lines of meeting of these principal sections are the axes, or principal diameters of the ellipsoid. The point where the three planes meet is the center.
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Century Dictionary and Cyclopedia
• n ellipsoid In geometry, a solid figure all plane sections of which are ellipses or circles.
• n ellipsoid In anthropology, a cranium the norma verticalis of which has an ellipsoidal form.
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Chambers's Twentieth Century Dictionary
• Ellipsoid (math.) a surface every plane section of which is an ellipse
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## Etymology

Webster's Revised Unabridged Dictionary
Ellipse, + -oid,: cf. F. ellipsoide,
Chambers's Twentieth Century Dictionary
L.,—Gr. elleipsiselleipein, to fall short—en, in, leipein, to leave.

## Usage

### In literature:

It is a roomy niche, shaped like a flattened ellipsoid, the length of which reaches eighty to a hundred millimetres.
"The Wonders of Instinct" by J. H. Fabre
The earth was like a swinging swaying censer, a ball of incense, an ellipsoidal fall.
"A Portrait of the Artist as a Young Man" by James Joyce
The nucleus is large and ellipsoidal, with characteristic longitudinal markings of chromatin.
"Marine Protozoa from Woods Hole" by Gary N. Calkins
The two lateral zones, which occupy the greater part of the demi-ellipsoid, have a perfect continuity of surface.
"Social Life in the Insect World" by J. H. Fabre
The sphere became an ellipsoid.
"Invaders from the Infinite" by John Wood Campbell
Elliptical: oblong-oval, the ends equally rounded, together forming an even ellipsoid.
"Explanation of Terms Used in Entomology" by John. B. Smith
Grain is tightly enclosed by the hardened glume and its palea and is oblong or ellipsoid.
"A Handbook of Some South Indian Grasses" by Rai Bahadur K. Ranga Achariyar
The spores are ellipsoid, 9-11x5-6u.
"The Mushroom, Edible and Otherwise" by M. E. Hard
Sporangia globose or ovoid to ellipsoid or oblong, erect or sometimes inclined or even nodding.
"The Myxomycetes of the Miami Valley, Ohio" by A. P. Morgan
The form of the latter is at first globular, then ellipsoid, and more or less curved.
"Fungi: Their Nature and Uses" by Mordecai Cubitt Cooke
The children are invariably delighted with both hemispheres and ellipsoids, and need no stimulus from the kindergartner in their use.
"Froebel's Gifts" by Kate Douglas Wiggin
Spores thin-walled, ellipsoidal, violaceous, plicate-rugose, 14-16 x 11-12 mu.
"The North American Slime-Moulds" by Thomas H. (Thomas Huston) MacBride
Occupying most of it were three grey, ellipsoidal objects, smooth and featureless.
"The Thing in the Attic" by James Benjamin Blish
In the bird they are larger, ellipsoidal in shape and have a large nucleus in the centre of the cell.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 1" by Various
The residual force just described is not limited to the case of an ellipsoidal body.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7" by Various
They are elongate ellipsoidal in shape, about .4 by .18 mm.
"Handbook of Medical Entomology" by William Albert Riley
We may, however, assume the ellipsoid with three unequal axes to be an interpolation form.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 9" by Various
Similarly, the dielectric constants of a non-conducting crystal may be expressed by a sphere, spheroid or ellipsoid.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 7" by Various
The bright orange-yellow fruit is round or ellipsoidal, about 1 in.
"Encyclopaedia Britannica, 11th Edition, Volume 15, Slice 8" by Various
Finally the nuclear disc assumes an ellipsoidal form and becomes the nuclear body.
"The Works of Francis Maitland Balfour, Volume 1" by Francis Maitland Balfour
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### In news:

Improvements to the VARI*LITE® Series 1000TM product line have resulted in higher output and greater brightness from Vari-Lite Inc.'s award-winning VL1000TM ellipsoidal reflector spotlight.
The Opti Profile ellipsoidal-style fixture projects up to 40 feet.
Vulcan 2/3 jacketed steam kettles have an ellipsoidal bottom that provides a larger heat surface and gentle, uniform steam for more consistently prepared soups, sauces and stews.
1930s Ellipsoidals A historic year for stage lighting, 1933 brought with it the ellipsoidal reflector spotlight (ERS).
Vari-Lite Europe has taken delivery of its first VL1000™ ellipsoidal reflector spotlight units.
The Pittsburgh Symphony Orchestra will perform this week at Beijing's new National Centre for the Performing Arts, a massive ellipsoid structure covering nearly 330,000 square feet and nicknamed "The Egg.".
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### In science:

The resulting lightcurve has marked deviations from the expected ellipsoidal shape.
A TiO study of the dwarf nova IP Pegasi
Depending on the geometry, this irregular heating process can lead to a substantial thickening of the disc and to a velocity ellipsoid that is signiﬁcantly different than in the solar neighbourhood.
Disc heating in NGC 2985
Cross terms – i.e. tilting of the velocity ellipsoid – will on average be zero along each line of sight through a galactic disc.
Disc heating in NGC 2985
The upper dashed line indicates an isotropic σz = σR velocity ellipsoid.
Disc heating in NGC 2985
Observed velocity ellipsoid ratios as a function of morphological RC3 type.
Disc heating in NGC 2985
In two recent papers [1, 2], geometric probability techniques were developed to calculate the functions P3 (s) which describe the probability density of ﬁnding a random distance s separating two random points distributed in a uniform sphere and in a uniform ellipsoid.
Random Distance Distribution for Spherical Objects: General Theory and Applications to n-Dimensional Physics
The Gaussian solution has been generalized to ellipsoidal expansions in , that provides analytic insight into the physics of non-central heavy ion collisions .
Simple solutions of relativistic hydrodynamics for longitudinally expanding systems
The spherically symmetric Gaussian solution has been generalized to ellipsoidally symmetric expansions , that provided simple analytic insight into the observables of non-central heavy-ion collisions .
Simple solutions of relativistic hydrodynamics for cylindrically symmetric systems
Gregory, Thompson, and Tifft discovered that the distribution of the rotation axes for both the spiral and ellipsoid galaxies of the ﬁlament-like Perseus-Pisces supercluster is bimodal.
General Relativity Requires Absolute Space and Time
These acceleration ratios were obtained by computing the equatorial plane potential of ellipsoidal halos with isosurface-density axis ratios a : b : c and ma jor axis density proﬁles ρ(r) ∝ (1 + (r/rc)2 )−1 .
On the Spiral Structure of NGC 2915 and Dark Matter
On the other hand, it is well known that in Newtonian gravity numerous results have been obtained for the case in which a rotating ﬂuid in equilibrium has an ellipsoidal shape .
Ellipsoidal shapes in general relativity: general definitions and an application
In the present work we will constrain our attention to those rapidly rotating conﬁgurations in general relativity, for which there is a natural way for imposing the restriction that the surface of the considered ob ject is ellipsoidal.
Ellipsoidal shapes in general relativity: general definitions and an application
Using the approach presented in this paper the matching surface between the interior and exterior region may be conveniently chosen to be the ellipsoid representing the boundary of the rotating ﬂuid body.
Ellipsoidal shapes in general relativity: general definitions and an application
In the Euclidean geometry of ﬂat space the notion of an ellipsoid is clear and easily understood.
Ellipsoidal shapes in general relativity: general definitions and an application
In such spaces the coordinate surfaces ρ = const represent the analogue of a one-parameter congruence of confocal Euclidean ellipsoids of revolution.
Ellipsoidal shapes in general relativity: general definitions and an application
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