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hyperbolic sphere

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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

  • Sphere packing — In mathematics, sphere packing problems are problems concerning arrangements of non overlapping identical spheres which fill a space. Usually the space involved is three dimensional Euclidean space. However, sphere packing problems can be… …   Wikipedia

  • 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 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 link — In mathematics, a hyperbolic link is a link in the 3 sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component.As a… …   Wikipedia

  • Sphere-world — The idea of a sphere world was constructed by Henri Poincaré while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.Poincaré asks us to imagine a… …   Wikipedia

  • 3-sphere — Stereographic projection of the hypersphere s parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles …   Wikipedia

  • n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …   Wikipedia

  • N-sphere — can project a sphere s surface to a plane, it can also project a 3 sphere s surface into 3 space. This image shows three coordinate directions projected to 3 space:parallels (red), meridians (blue) and hypermeridians (green).Due to the conformal… …   Wikipedia

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