“non-Euclidean geometry”的概念、定义、翻译、参考文献-科学参考

non-Euclidean geometry

Physics

A type of geometry that does not comply with the basic postulates of Euclidean geometry, particularly a form of geometry that does not accept Euclid’s postulate that only one straight line can be drawn through a point in space parallel to a given straight line. Several types of non-Euclidean geometry exist.

Mathematics

After unsuccessful attempts had been made at proving that the parallel postulate could be deduced from the other postulates of Euclid’s, the matter was settled by the discovery of non-Euclidean geometries by Lobachevsky and Bolyai. In these, all Euclid’s postulates hold except the parallel postulate. In hyperbolic geometry, given a point not on a given line, there are at least two lines through the point parallel to the line (i.e. these parallel lines do not intersect the given line). In elliptic geometry, given a point not on a given line, there are no parallels through the point. See elliptic plane, hyperbolic plane, neutral geometry.

Philosophy

See geometry.

单词	non-Euclidean geometry
释义	non-Euclidean geometry Physics A type of geometry that does not comply with the basic postulates of Euclidean geometry, particularly a form of geometry that does not accept Euclid’s postulate that only one straight line can be drawn through a point in space parallel to a given straight line. Several types of non-Euclidean geometry exist. Mathematics After unsuccessful attempts had been made at proving that the parallel postulate could be deduced from the other postulates of Euclid’s, the matter was settled by the discovery of non-Euclidean geometries by Lobachevsky and Bolyai. In these, all Euclid’s postulates hold except the parallel postulate. In hyperbolic geometry, given a point not on a given line, there are at least two lines through the point parallel to the line (i.e. these parallel lines do not intersect the given line). In elliptic geometry, given a point not on a given line, there are no parallels through the point. See elliptic plane, hyperbolic plane, neutral geometry. Philosophy See geometry.
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