elliptic geometry


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 given line is parallel to that line. It also states that while any straight line of finite length can be extended indefinitely, all straight lines are the same length. Though many of elliptic geometry's theorems are identical to those of Euclidean geometry, others differ (e.g., the angles in a triangle add up to more than 180°). It can most easily be pictured as geometry done on the surface of a sphere where all lines are great circles.

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Universalium. 2010.

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 — noun (mathematics) a non Euclidean geometry that regards space as like a sphere and a line as like a great circle Bernhard Riemann pioneered elliptic geometry • Syn: ↑Riemannian geometry • Topics: ↑mathematics, ↑math, ↑maths …   Useful english dictionary

  • 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


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