- Poincaré disk
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The hyperbolic plane, viewed as a disk so that Euclidean circles and lines Euclidean-perpendicular to the disks surface are hyperbolic lines.
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Poincaré disk
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Poincaré disk model — Poincaré disc model of great rhombitruncated {3,7} tiling … Wikipedia
Poincaré model — can refer to:*Poincaré disk model, a model of n dimensional hyperbolic geometry *Poincaré half plane model, a model of two dimensional hyperbolic geometry … Wikipedia
Poincaré metric — In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry… … Wikipedia
Poincaré half-plane model — Stellated regular heptagonal tiling of the model.In non Euclidean geometry, the Poincaré half plane model is the upper half plane, together with a metric, the Poincaré metric, that makes it a model of two dimensional hyperbolic geometry.It is… … Wikipedia
Unit disk — For other uses, see Disc (disambiguation). An open Euclidean unit disk In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1 … Wikipedia
Klein model — In geometry, the Klein model, also called the projective model, the Beltrami–Klein model, the Klein–Beltrami model and the Cayley–Klein model, is a model of n dimensional hyperbolic geometry in which the points of the geometry are in an n… … Wikipedia
Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… … Wikipedia
Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall … Wikipedia
Möbius transformation — Not to be confused with Möbius transform or Möbius function. In geometry, a Möbius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − … Wikipedia
non-Euclidean geometry — geometry based upon one or more postulates that differ from those of Euclid, esp. from the postulate that only one line may be drawn through a given point parallel to a given line. [1870 75; NON + EUCLIDEAN] * * * Any theory of the nature of… … Universalium
