Coordinate systems for the hyperbolic plane (original) (raw)

In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of coordinatizing the plane in hyperbolic geometry are used. This article tries to give an overview of several coordinate systems in use for the two-dimensional hyperbolic plane. In the descriptions below the constant Gaussian curvature of the plane is −1. Sinh, cosh and tanh are hyperbolic functions.