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hyperbolic surface

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  • 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 soccerball — The hyperbolic soccerball is a tiling of a surface frequently used as a manipulative for studying the properties of hyperbolic geometry. It is an embedding of the order 7 truncated triangular tiling into Euclidean space.DescriptionJust as… …   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 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 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 quaternion — In mathematics, a hyperbolic quaternion is a mathematical concept first suggested by Alexander MacFarlane in 1891 in a speech to the American Association for the Advancement of Science. The idea was criticized for its failure to conform to… …   Wikipedia

  • Surface de Bolza — Représentation en perspective de l équation y2 = x5 − x dans . En mathématiques, la surface de Bolza (du nom d Oskar Bolza) est une surface de Riemann compacte de g …   Wikipédia en Français

  • Surface subgroup conjecture — In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3 manifold with infinite fundamental group has a surface subgroup. By surface subgroup we mean the fundamental… …   Wikipedia

  • hyperbolic paraboloid — noun Date: 1842 a saddle shaped quadric surface whose sections by planes parallel to one coordinate plane are hyperbolas while those sections by planes parallel to the other two are parabolas if proper orientation of the coordinate axes is… …   New Collegiate Dictionary

  • hyperbolic paraboloid — noun : a saddle shaped quadric surface whose sections by planes parallel to one coordinate plane are hyperbolas while those sections by planes parallel to the other two are parabolas if proper orientation of the coordinate axes is assumed …   Useful english dictionary

  • Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia

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