page_title: Poincaré disk model
section_title: Relation to other models of hyperbolic geometry
hierarchical_section_title: Poincaré disk model / Relation to other models of hyperbolic geometry
caption_attribution_description: English: Poincaré disk, hemispherical and hyperboloid models are related by central projection from −1. Klein disk model is vertical projection from hemispheric model. Poincaré half-plane model here projected from the hemisphere model by rays from left end of Poincaré disk model.
context_page_description: In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all circular arcs contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.
  The isometry group of the disk model is given by the special unitary group SU.
  Along with the Klein model and the Poincaré half-space model, it was proposed by Eugenio Beltrami who used these models to show that hyperbolic geometry was equiconsistent with Euclidean geometry. It is named after Henri Poincaré, because his rediscovery of this representation fourteen years later became better known than the original work of Beltrami.
  The Poincaré ball model is the similar model for 3 or n-dimensional hyperbolic geometry in which the points of the geometry are in the n-dimensional unit ball.
caption: the Poincaré disk model  (line P), and their relations with the other models
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