In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two-dimensional space, for any given line R and point P ...
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a non-Euclidean geometry that rejects the validity of Euclid`s fifth, the `parallel,` postulate. Simply stated, this Euclidean postulate is: through ... [3 related articles]
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http://www.britannica.com/eb/a-z/h/91
One of the two main types of non-Euclidean geometry and the first to be discovered. It is concerned with saddle-surfaces, which have negative curvature and on which the geodesics are hyperbolas. In hyperbolic geometry, contrary to the parallel postulate, there exists a line m and a point p not on m ...
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[
n] - a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane
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http://www.webdictionary.co.uk/definition.php?query=hyperbolic%20geometry
noun a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane
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the branch of non-Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that two distinct lines may be drawn parallel to a given line through a point not on the given line. Cf. Riemannian geometry.
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https://www.infoplease.com/dictionary/hyperbolic-geometry
a non-Euclidean geometry based on a saddle-shaped plane, in which there are no parallel lines and the angles of a triangle sum to less than 180°
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