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Definition of Non-Euclidean geometry
1. Noun. (mathematics) geometry based on axioms different from Euclid's. "Non-Euclidean geometries discard or replace one or more of the Euclidean axioms"
Generic synonyms: Geometry
Specialized synonyms: Hyperbolic Geometry, Elliptic Geometry, Riemannian Geometry
Definition of Non-Euclidean geometry
1. Noun. (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. ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Non-Euclidean Geometry
Literary usage of Non-Euclidean geometry
Below you will find example usage of this term as found in modern and/or classical literature:
1. The American Mathematical Monthly by Mathematical Association of America (1901)
""This truth, really self-evident yet often not taken to heart, applied to Euclidean
and non-Euclidean geometry, leads to the somewhat paradoxical result, ..."
2. Science by American Association for the Advancement of Science (1904)
"In this new or non-Euclidean geometry, on the contrary, the sum of the angles in
every ... In this non-Euclidean geometry parallels continually approach. ..."
3. The Encyclopedia Americana: A Library of Universal Knowledge (1919)
"In this a non-Euclidean geometry is for the first time propounded without any
logical misgivings. The system treated is the same as that of Lobachevsky. ..."
4. Development of Mathematics in the 19th Century by Felix Klein, Robert Hermann (1979)
"... AND non-Euclidean geometry IN R FROM THE KLEINIAN VIEWPOINT 1. INTRODUCTION Klein
was a master at finding interrelations. In his day he was famous for ..."
5. Science by American Association for the Advancement of Science (1904)
""The memoir of pure analysis, entitled 'General Geometry of Spaces' is a
generalization of the formulas of Euclidean or non-Euclidean geometry of three ..."
6. The Evanston Colloquium: Lectures on Mathematics Delivered from Aug. 28 to by Felix Klein (1893)
"There are three points of view from which non-Euclidean geometry has been ...
Thus they build up a system of non- Euclidean geometry in which the length of ..."
7. A History of Elementary Mathematics: With Hints on Methods of Teaching by Florian Cajori (1917)
"non-Euclidean geometry. — The history of this subject centres almost wholly in
the theory of parallel lines. Preliminary to the discussion of the ..."
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