# ellipsoid

ellipsoid
/i lip"soyd/, n.
1. Geom. a solid figure all plane sections of which are ellipses or circles. Typical equation: (x2/a2) + (y2/b2) + (z2/c2) = 1.
2. ellipsoidal.
[1715-25; < F ellipsoïde. See ELLIPSE, -OID]

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closed surface of which all plane cross sections are either ellipses (ellipse) or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the centre.

If a, b, and c are the principal semiaxes, the general equation of such an ellipsoid is x2/a2 + y2/b2 + z2/c2 = 1. A special case arises when a = bc: then the surface is a sphere, and the intersection with any plane passing through it is a circle. If two axes are equal, say a = b, and different from the third, c, then the ellipsoid is an ellipsoid of revolution, or spheroid (see the figure—>), the figure formed by revolving an ellipse about one of its axes. If a and b are greater than c, the spheroid is oblate; if less, the surface is a prolate spheroid.

An oblate spheroid is formed by revolving an ellipse about its minor axis; a prolate, about its major axis. In either case, intersections of the surface by planes parallel to the axis of revolution are ellipses, while intersections by planes perpendicular to that axis are circles.

Isaac Newton (Newton, Sir Isaac) predicted that because of the Earth's rotation, its shape should be an ellipsoid rather than spherical, and careful measurements confirmed his prediction. As more accurate measurements became possible, further deviations from the elliptical shape were discovered. See also .

Often an ellipsoid of revolution (called the reference ellipsoid) is used to represent the Earth in geodetic calculations, because such calculations are simpler than those with more complicated mathematical models. For this ellipsoid, the difference between the equatorial radius and the polar radius (the semimajor and semiminor axes, respectively) is about 21 km (13 miles), and the flattening is about 1 part in 300.

Robert Osserman

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Universalium. 2010.

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### Look at other dictionaries:

• Ellipsoid — El*lip soid, n. [Ellipse + oid: cf. F. ellipsoide.] (Geom.) A solid, all plane sections of which are ellipses or circles. See {Conoid}, n., 2 (a) . [1913 Webster] Note: The ellipsoid has three principal plane sections, a, b, and c, each at right… …   The Collaborative International Dictionary of English

• Ellipsoid — El*lip soid, Ellipsoidal El lip*soi dal, a. Pertaining to, or shaped like, an ellipsoid; as, ellipsoid or ellipsoidal form …   The Collaborative International Dictionary of English

• Ellipsoïd — (griech., »ellipsenähnlich«), eine geschlossene krumme Fläche, ungefähr wie die Oberfläche eines Eies, wird folgendermaßen erhalten: man denke sich von einem Punkt O (s. Figur), dem Mittelpunkt, ausgehend drei gerade, zueinander senkrechte Linien …   Meyers Großes Konversations-Lexikon

• ellipsoid — [e΄lip soid′ le lip′soid΄, ilip′soid] n. [Fr ellipsoïde: see ELLIPSE & OID] Geom. 1. a solid formed by rotating an ellipse around either axis: its plane sections are all ellipses or circles 2. the surface of such a solid adj. of or shaped like an …   English World dictionary

• Ellipsŏid — (v. gr.), allgemeinere Bedeutung von Späroid, ein Körper, in welchem nicht, wie im Sphäroid, 2 Achsen gleich sind …   Pierer's Universal-Lexikon

• Ellipsoid — Ellipsoid, s. Flächen zweiten Grades und Erde …   Lexikon der gesamten Technik

• Ellipsoid — Ellipsoīd, eine krumme Oberfläche zweiter Ordnung, deren Durchschnitte mittels einer Ebene durch eine Symmetrieachse Ellipsen oder (beim Rotations E. oder elliptischen Sphäroid) zum Teil auch Kreise bilden …   Kleines Konversations-Lexikon

• ellipsoid — 1721 (n.); 1861 (adj.); see ELLIPSE (Cf. ellipse) + OID (Cf. oid) …   Etymology dictionary

• Ellipsoid — This article is about the shape. For the type of theatrical spotlight, see ellipsoidal reflector spotlight. For the surface that approximates the figure of the Earth, see reference ellipsoid. triaxial redirects here. For the electrical cable, see …   Wikipedia

• Ellipsoid — Triaxiales Ellipsoid mit (a,b,c) = (4,2,1) Ein Ellipsoid ist die drei oder mehrdimensionale Entsprechung einer Ellipse. Bekannte Beispiele sind die Erde und der Rugbyball als Rotationsellipsoid. Inhaltsverzeichnis …   Deutsch Wikipedia