elliptic geometry

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Related to elliptic geometry: hyperbolic geometry

elliptic geometry

n
(Mathematics) another name for Riemannian geometry
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 elliptic geometry - (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"Riemannian geometrymath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementnon-Euclidean geometry - (mathematics) geometry based on axioms different from Euclid's; "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"
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(4) To demolish Einstein's theories of relativity (in elliptic geometry), you could go back and prove the parallel postulate, bringing down not only Einstein, but all of the non-Euclidean geometries, as well.
As in Non-Euclidean Geometry, there are models that validate the hyperbolic geometric and of course invalidate the Euclidean geometry, or models that validate the elliptic geometry and in consequence they invalidate the Euclidean geometry and the hyperbolic geometry.
While in the Riemannian geometry, called elliptic geometry, the fifth Euclidean postulate is also invalidated as follows: there is no parallel to a given line passing through an exterior point.

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