Hyperbolic geometry

A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), as well as two diverging ultra-parallel lines

Rhombitriheptagonal tiling of the hyperbolic plane, seen in the Poincaré disk model

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry. In hyperbolic geometry the parallel postulate of Euclidean geometry is replaced with:

Hyperbolic plane geometry is also the geometry of saddle surface or pseudospherical surfaces, surfaces with a constant negative Gaussian curvature.

单词	Lobachevskian
释义	Lobachevskian 英语百科 Hyperbolic geometry In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry. In hyperbolic geometry the parallel postulate of Euclidean geometry is replaced with: Hyperbolic plane geometry is also the geometry of saddle surface or pseudospherical surfaces, surfaces with a constant negative Gaussian curvature.
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