as a ruler in Euclidean geometry A hyperbolic ruler cannot perform Euclidean geometry constructions In hyperbolic geometry, constructions that can be...

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric...

geometry in the nineteenth century stimulated the development of non-Euclidean geometry generally, including hyperbolic geometry. Elliptic geometry has...

geometry is not an absolute geometry. The theorems of absolute geometry hold in hyperbolic geometry, which is a non-Euclidean geometry, as well as in...

the topic of hyperbolic geometry. Sometimes the qualificative "real" is added to distinguish it from complex hyperbolic spaces. Hyperbolic space serves...

Projective geometry can also be seen as a geometry of constructions with a straight-edge alone, excluding compass constructions, common in straightedge...

satisfying certain properties abstracted from classical hyperbolic geometry. The notion of a hyperbolic group was introduced and developed by Mikhail Gromov (1987)...

In mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic...

triangles in hyperbolic geometry is positive, and the defect of triangles in Euclidean geometry is zero. The area of a triangle in hyperbolic geometry is bounded...