### Definition of Hyperbolic geometry

1. Noun. (mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane. "Karl Gauss pioneered hyperbolic geometry"

Category relationships: Math, Mathematics, Maths
Generic synonyms: Non-euclidean Geometry

### Hyperbolic Geometry Pictures

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### Lexicographical Neighbors of Hyperbolic Geometry

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### Literary usage of Hyperbolic geometry

Below you will find example usage of this term as found in modern and/or classical literature:

1. Projective Geometry by Oswald Veblen, John Wesley Young (1918)
"Interpretation of hyperbolic geometry in the inversion plane. Although the theory of conies touching a fixed conic in pairs of points has not been taken up ..."

2. A Treatise on Universal Algebra: With Applications by Alfred North Whitehead (1898)
"In fact for such a case in elliptic geometry the line XiX., would then be imaginary ; and in hyperbolic geometry a\ and a^ would lie outside the absolute. ..."

3. Geometry of Riemannian Spaces by Elie Cartan (1983)
"TWO DIMENSIONAL hyperbolic geometry 125. The formulae representing the ... The Euclidean postulate is not true for hyperbolic geometry; for through a point ..."

4. Non-Euclidean Geometry by Henry Parker Manning (1901)
"CHAPTER TI THE hyperbolic geometry WE have now the hypothesis of the acute angle. Two lines in a plane perpendicular to a third diverge on either side of ..."

5. A Short Account of the History of Mathematics by Walter William Rouse Ball (1908)
"This leads to a geometry of two dimensions, called elliptic geometry, analogous to the hyperbolic geometry, but characterised by the fact that through a ..."

6. The Encyclopaedia Britannica: A Dictionary of Arts, Sciences, and General by Thomas Spencer Baynes (1888)
"... great interest because it shows us that Gauss was then in full possession of the most important propositions of what is now called hyperbolic geometry. ..."

7. Science by American Association for the Advancement of Science (1897)
"From this letter it is perfectly clear that in 1799, so far from having the remotest idea of a hyperbolic geometry, or any non-Euclidean geometry, ..."