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Poincaré disk model

In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or diameters of the unit circle.

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Overview

History

Lines and distance

Metric and curvature

Construction of lines

Angles

Cycles

Relation to other models of hyperbolic geometry

Artistic realizations

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Map overview Semantic statistics

Poincaré disk model

Nodes83
Edges82
Triples63
Avg. degree1.98
Density0.024096
Components1

How this topic connects Entity context

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Poincaré disk model

Top relations

related to Artistic realizations · 15
Poincaré disk model → According, Bruno Ernst, Canadian, Circle Limit, Circle Limit III, Circle Limit IV, Discussions, Escher, Escher's, Harold Scott MacDonald Coxeter, Heaven, Hell, HyperRogue, IV, Poincaré
related to Relation to the hyperboloid model · 7
Poincaré disk model → Beltrami, For Cartesian, If, Klein, Poincaré, The, The Poincaré
related to Relation to the Klein disk model · 7
Poincaré disk model → An, Euclidean, Klein, Poincaré, The, The Beltrami, The Klein
related to Relation to the Poincaré half-plane model · 7
Poincaré disk model → Cayley, If, In, Möbius, Poincaré, The Poincaré, Under
related to Angles · 5
Poincaré disk model → If, Klein, Poincaré, Since, We
related to Horocycles · 5
Poincaré disk model → Euclidean, In, It, Poincaré, The
related to Metric and curvature · 5
Poincaré disk model → Cartesian, Euclidean, In, Poincaré, The
related to Cycles · 4
Poincaré disk model → Euclidean, In, On, Poincaré
related to External links · 4
Poincaré disk model → Media, Poincaré, Wikimedia Commons, Wiktionary-logo-en-v2
related to By analytic geometry · 3
Poincaré disk model → Given, In, Poincaré

Important terminology Word statistics

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Important terminology

disk model poincaré hyperbolic circle displaystyle points point euclidean klein geometry two boundary plane line frac given center lines one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Poincaré disk modelis astereographic projection.An advantage of the Klein disk model is that lines in this model are Euclidean straight chords0.90text
Poincaré disk modelrelated to AnglesWe0.60section
Poincaré disk modelrelated to AnglesSince0.60section
Poincaré disk modelrelated to AnglesKlein0.60section
Poincaré disk modelrelated to AnglesPoincaré0.60section
Poincaré disk modelrelated to AnglesIf0.60section
Poincaré disk modelrelated to Artistic realizationsEscher0.60section
Poincaré disk modelrelated to Artistic realizationsDiscussions0.60section
Poincaré disk modelrelated to Artistic realizationsCanadian0.60section
Poincaré disk modelrelated to Artistic realizationsHarold Scott MacDonald Coxeter0.60section
Poincaré disk modelrelated to Artistic realizationsEscher's0.60section
Poincaré disk modelrelated to Artistic realizationsCircle Limit0.60section

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