# elliptic geometry

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elliptic geometry
noun
(mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle
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Bernhard Riemann pioneered elliptic geometry

Topics: ↑mathematics, ↑math, ↑maths
Hypernyms: ↑non-Euclidean geometry

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noun
: geometry that adopts all of Euclid's axioms except the parallel axiom which is replaced by the axiom that through a point in a plane there pass no lines that do not intersect a given line in the plane

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elliptic geometry or elliptic space noun
Riemannian geometry or space
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Main Entry:ellipse

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elliptic geometry,
a system of geometry in which two or more lines passing through a point in a plane always intersect a given line in the plane (contrasted with hyperbolic geometry).

Useful english dictionary. 2012.

### Look at other dictionaries:

• Elliptic geometry — (sometimes known as Riemannian geometry) is a non Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p.Elliptic geometry, like hyperbolic geometry, violates Euclid s parallel… …   Wikipedia

• elliptic geometry — Non Euclidean geometry that rejects Euclid s fifth postulate (the parallel postulate) and modifies his second postulate. It is also known as Riemannian geometry, after Bernhard Riemann. It asserts that no line passing through a point not on a… …   Universalium

• elliptic geometry. — See Riemannian geometry (def. 1). * * * …   Universalium

• elliptic geometry. — See Riemannian geometry (def. 1) …   Useful english dictionary

• elliptic space — elliptic geometry or elliptic space noun Riemannian geometry or space • • • Main Entry: ↑ellipse …   Useful english dictionary

• geometry — /jee om i tree/, n. 1. the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties… …   Universalium

• Elliptic curve — In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O . An elliptic curve is in fact an abelian variety mdash; that is, it has a multiplication defined algebraically with… …   Wikipedia

• Elliptic complex — In mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex… …   Wikipedia

• Elliptic point — In differential geometry, an elliptic point on a regular surface in R 3 is a point p at which the Gaussian curvature K ( p ) > 0 or equivalently, the principal curvatures k 1 and k 2 have the same sign …   Wikipedia

• non-Euclidean geometry — geometry based upon one or more postulates that differ from those of Euclid, esp. from the postulate that only one line may be drawn through a given point parallel to a given line. [1870 75; NON + EUCLIDEAN] * * * Any theory of the nature of… …   Universalium