Research topic: non-Euclidean geometry

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non-Euclidean geometry

The Columbia Encyclopedia, Sixth Edition
non-Euclidean geometry branch of geometry in which the fifth postulate of Euclidean geometry, which allows one and only one line parallel to a given line through a given external point, is replaced by one of two alternative postulates. Allowing two parallels through any external point, the first alternative to Euclid 's fifth postulate, leads to the hyperbolic geometry developed by the Russian N. I. Lobachevsky in 1826 and independently by the Hungarian Janos Bolyai in 1832. The second alternative, which allows no parallels through any external point, leads to the elliptic geometry... Read more
non-Euclidean geometry
...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...relativity . Nikolay Lobachevsky , Bernhard Riemann . non-Euclidean geometry ... Read more
non-Euclidean
non-Eu·clid·e·an / ˌnän yoōˈklidēən / • adj. Geom. denying or going beyond Euclidean principles in geometry, esp. in contravening the postulate that only one line through a given point can be parallel to a given line. Read more

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Euclidean & Non-Euclidean Geometries Part 1

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