non-euclidean geometries

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Definition of non-euclidean geometries in English English dictionary

Related Terms

non-Euclidean geometries

plural form of non-Euclidean geometry

non-Euclidean geometry

Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience

non-Euclidean geometry

Any theory of the nature of geometric space differing from the traditional view held since Euclid's time. These geometries arose in the 19th century when several mathematicians working independently explored the possibility of rejecting Euclid's parallel postulate. Different assumptions about how many lines through a point not on a given line could be parallel to that line resulted in hyperbolic geometry and elliptic geometry. Mathematicians were forced to abandon the idea of a single correct geometry; it became their task not to discover mathematical systems but to create them by selecting consistent axioms and studying the theorems that could be derived from them. The development of these alternative geometries had a profound impact on the notion of space and paved the way for the theory of relativity. See also Nikolay Lobachevsky, Bernhard Riemann

non-euclidean geometry

geometry based on axioms different from Euclid's

Hyphenation

non-Eu·clid·e·an geometries