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In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature. It is hyperbolic geometry in more than 2 dimensions, and is distinguished from Euclidean spaces with zero curvature that define the Euclidean geometry, and elliptic geometry that have a constant positive curvature. When embedded to a Euclidean space (of a higher dimension), every point of a hyperbolic space is a saddle point. Another distinctive property is the amount of space covered by the ''n''-ball in hyperbolic ''n''-space: it increases exponentially with respect to the radius of the ball for large radii, rather than polynomially. ==Formal definition== Hyperbolic ''n''-space, denoted H''n'', is the maximally symmetric, simply connected, ''n''-dimensional Riemannian manifold with a constant negative sectional curvature. Hyperbolic space is a space exhibiting hyperbolic geometry. It is the negative-curvature analogue of the ''n''-sphere. Although hyperbolic space H''n'' is diffeomorphic to R''n'', its negative-curvature metric gives it very different geometric properties. Hyperbolic 2-space, H2, is also called the hyperbolic plane. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hyperbolic space」の詳細全文を読む スポンサード リンク
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