Definify.com
Webster 1913 Edition
Ellipsoid
El-lip′soid
,Noun.
[
Ellipse
+ -oid
: cf. F. ellipsoide
.] (Geom.)
☞ 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.
Webster 1828 Edition
Ellipsoid
ELLIPS'OID
,Noun.
Definition 2024
Ellipsoid
Ellipsoid
See also: ellipsoid
German
Alternative forms
Noun
Ellipsoid n (genitive Ellipsoides or Ellipsoids, plural Ellipsoide)
- ellipsoid (surface all of whose cross sections are elliptic or circular)
Declension
Declension of Ellipsoid
| singular | plural | ||||
|---|---|---|---|---|---|
| indef. | def. | noun | def. | noun | |
| nominative | ein | das | Ellipsoid | die | Ellipsoide |
| genitive | eines | des | Ellipsoides, Ellipsoids |
der | Ellipsoide |
| dative | einem | dem | Ellipsoid, Ellipsoide1 |
den | Ellipsoiden |
| accusative | ein | das | Ellipsoid | die | Ellipsoide |
1Now uncommon, see notes
ellipsoid
ellipsoid
See also: Ellipsoid
English
Noun
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 x2/a2 + y2/b2 + z2/c2 = 0.
- 2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133,
- Polarizability can be imagined as a three-dimensional 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 notes
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.
Related terms
Derived terms
- ellipsoid of revolution
- ellipsoid geodesic
- ellipsoid method
- ellipsoid packing
- scalene ellipsoid (rare)
- triaxial ellipsoid
Translations
surface all of whose cross sections are elliptic or circular
|
Adjective
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 terms
Translations
shaped like an ellipse — see elliptical
of or pertaining to an ellipse
|
See also
Swedish
Noun
ellipsoid c
Declension
| Inflection of ellipsoid | ||||
|---|---|---|---|---|
| Singular | Plural | |||
| Indefinite | Definite | Indefinite | Definite | |
| Nominative | ellipsoid | ellipsoiden | ellipsoider | ellipsoiderna |
| Genitive | ellipsoids | ellipsoidens | ellipsoiders | ellipsoidernas |