ellipsoid
See also: Ellipsoid
Contents
EnglishEdit
EtymologyEdit
NounEdit
ellipsoid (plural ellipsoids)
 (mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x^{2}/a^{2} + y^{2}/b^{2} + z^{2}/c^{2} = 0.
 2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133,
 Polarizability can be imagined as a threedimensional ellipsoid centred on the centre of the molecule, as shown in Figure 10.4.
 2004, Alfred Leick, GPS Satellite Surveying, 3rd Edition, page 367,
 Because only ellipsoids of rotation have been adopted in practical geodesy and surveying and triaxial ellipsoids have been limited to theoretical studies, we will use the term ellipsoid for brevity to mean ellipsoid of rotation.
 2010, Jan Van Sickle, Basic GIS Coordinates, 2nd Edition, page 73,
 As mentioned before, modern geodetic datums rely on the surfaces of geocentric ellipsoids to approximate the surface of the earth.
 2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133,
 (geography) Such a surface used as a model of the shape of the earth.

Here the geoid is thirty meters below the ellipsoid.

Usage notesEdit
The general case, with semiaxes a, b and c all different, is a triaxial ellipsoid (more rarely, scalene ellipsoid). If two are the same, say b = c, the result is an ellipsoid of revolution, which may be oblate (if a < b) or prolate (a > b). The degenerate case a = b = c is a sphere. An ellipsoid of revolution is also called a spheroid.
Derived termsEdit
 ellipsoid of revolution
 ellipsoid geodesic
 ellipsoid method
 ellipsoid packing
 scalene ellipsoid (rare)
 triaxial ellipsoid
Related termsEdit
TranslationsEdit
surface all of whose cross sections are elliptic or circular


See alsoEdit
AdjectiveEdit
ellipsoid (comparative more ellipsoid, superlative most ellipsoid)
 Shaped like an ellipse; elliptical.
 (mathematics) Of or pertaining to an ellipse; elliptic.
 (botany) Having the tridimensional shape of an ellipse rotated on its long axis.
Related termsEdit
TranslationsEdit
shaped like an ellipse — see elliptical
of or pertaining to an ellipse

having the shape of an ellipse rotated on its long axis

See alsoEdit
SwedishEdit
NounEdit
ellipsoid c
DeclensionEdit
Declension of ellipsoid  

Singular  Plural  
Indefinite  Definite  Indefinite  Definite  
Nominative  ellipsoid  ellipsoiden  ellipsoider  ellipsoiderna 
Genitive  ellipsoids  ellipsoidens  ellipsoiders  ellipsoidernas 