hyperbolic geometry

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• Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

• hyperbolic geometry — Geom. 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 …   Universalium

• hyperbolic geometry — 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… …   Useful english dictionary

• Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic… …   Wikipedia

• Hyperbolic motion — In geometry, a hyperbolic motion is a mapping of a model of hyperbolic geometry that preserves the distance measure in the model. Such a mapping is analogous to congruences of Euclidean geometry which are compositions of rotations and… …   Wikipedia

• Hyperbolic triangle — In mathematics, the term hyperbolic triangle has more than one meaning.In the foundations of the hyperbolic functions sinh, cosh and tanh, a hyperbolic triangle is a right triangle in the first quadrant of the Cartesian plane :{(x,y):x,y in… …   Wikipedia

• Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… …   Wikipedia

• Hyperbolic tree — In Web development jargon and information visualization, a hyperbolic tree (often shortened as hypertree) defines a visualization method for a graph inspired by hyperbolic geometry.Displaying hierarchical data as a tree suffers from visual… …   Wikipedia

• Hyperbolic 3-manifold — A hyperbolic 3 manifold is a 3 manifold equipped with a complete Riemannian metric of constant sectional curvature 1. In other words, it is the quotient of three dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely… …   Wikipedia

• Hyperbolic Dehn surgery — In mathematics, hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3 manifolds from a given cusped hyperbolic 3 manifold. Hyperbolic Dehn surgery exists only in dimension three and is one which distinguishes… …   Wikipedia

• geometry — /jee om i tree/, n. 1. the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties… …   Universalium