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Hyperbolic geometry

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

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Overview

Properties

Standardized Gaussian curvature

History

Physical realizations of the hyperbolic plane

Models of the hyperbolic plane

Isometries of the hyperbolic plane

In art

Homogeneous structure

Bibliography

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Hyperbolic geometry

Nodes208
Edges207
Triples219
Avg. degree1.99
Density0.009615
Components1

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Hyperbolic geometry

Top relations

related to Bibliography · 74
Hyperbolic geometry → A'Campo, Amer, American Mathematical Monthly, American Mathematical Society, Anderson, Asmus, Athanase, Athanase Papadopoulos, Berlin, Berlin-New York, Bull, Cannon, Co, Coxeter, David, De Gruyter Studies, Discontinuous, DOI, Edited, Elementary
related to External links · 26
Hyperbolic geometry → Bolyai, EMS Press, Encyclopedia, Eric, Frank NielsenStothers, Gauss, Glasgow, Hyperbolic, Hyperbolic Geometry University, Hyperbolic Planar TesselationsModels, Hyperbolic Plane, Illinois, Javascript, Lobachevskii, Lobachevsky Space, Mathematics, MathWorld, More, New Mexico, Poincaré Disk Model
related to history · 26
Hyperbolic geometry → Alfonso, Alhacen, BC, Dīn, Euclid's Elements, European, Foremost, Gersonides, Giovanni Gerolamo Saccheri, Haytham, Ibn, Johann Heinrich Lambert, John Wallis, Khayyam, Lambert, Legendre, Nasīr, Omar Khayyám, Proclus, Saccheri
related to Models of the hyperbolic plane · 13
Hyperbolic geometry → All, Beltrami, Despite, Euclidean, Gaussian, However, Klein, Lorentz, Of, Poincaré, There, These, Various
related to 19th-century developments · 12
Hyperbolic geometry → Bolyai, Carl Friedrich Gauss, Euclidean, Franz Taurinus, Gauss, In, János Bolyai, Lobachevsky, Nikolai Lobachevsky, Taurinus, The, Unlike
related to Relation to Euclidean geometry · 10
Hyperbolic geometry → All, Book One, Euclid's Elements, Euclidean, Further, Hyperbolic, Propositions, There, This, When
related to Philosophical consequences · 9
Hyperbolic geometry → Before, Critique, Euclid's Elements, Euclidean, Hobbes, Kant, Pure Reason, Spinoza, The
related to The hyperboloid model · 8
Hyperbolic geometry → Lorentz, Minkowski, One, Poincaré, Reynolds, The, This, Wilhelm Killing
related to Homogeneous structure · 7
Hyperbolic geometry → Hyperbolic, Many, Minkowski, R1, Riemannian, The, Timelike
related to Connection between the models · 6
Hyperbolic geometry → All, Euclidean, Gaussian, Hyperbolic, Once, The

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Important terminology

hyperbolic geometry model plane euclidean lines space two one poincaré curvature line models points distance point parallel hyperboloid klein disk

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hyperbolic geometryrelated to 19th-century developmentsIn0.60section
Hyperbolic geometryrelated to 19th-century developmentsNikolai Lobachevsky0.60section
Hyperbolic geometryrelated to 19th-century developmentsJános Bolyai0.60section
Hyperbolic geometryrelated to 19th-century developmentsCarl Friedrich Gauss0.60section
Hyperbolic geometryrelated to 19th-century developmentsFranz Taurinus0.60section
Hyperbolic geometryrelated to 19th-century developmentsUnlike0.60section
Hyperbolic geometryrelated to 19th-century developmentsEuclidean0.60section
Hyperbolic geometryrelated to 19th-century developmentsGauss0.60section
Hyperbolic geometryrelated to 19th-century developmentsTaurinus0.60section
Hyperbolic geometryrelated to 19th-century developmentsThe0.60section
Hyperbolic geometryrelated to 19th-century developmentsLobachevsky0.60section
Hyperbolic geometryrelated to 19th-century developmentsBolyai0.60section

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