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

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

and +sinh(t) respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions...

overstatement or exaggeration), or to hyperbolic geometry. The following phenomena are described as hyperbolic because they manifest hyperbolas, not because...

affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines...

non-Euclidean geometries, three "straight" segments (having zero curvature) also determine a triangle, for instance a spherical triangle or hyperbolic triangle...

stimulated the development of non-Euclidean geometry generally, including hyperbolic geometry. Elliptic geometry has a variety of properties that differ from...

topic of hyperbolic geometry. Sometimes the qualificative "real" is added to differentiate it from complex hyperbolic spaces, quaternionic hyperbolic spaces...

one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological...

In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...