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Hyperbolic motion

In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous group. This group is said to characterize the hyperbolic space. Such an approach to geometry was cultivated by Felix Klein in his Erlangen program. The idea of reducing geometry to its characteristic…

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Introduction of metric in the Poincaré half-plane model

Cartesian coordinatesPolar coordinatesCompositionDilationHypotenuse
12 related topics

Overview

GeometryIsometricAutomorphismsHyperbolic spaceContinuous group
24 related topics

Motions on the hyperbolic plane

MotionTransformationRotationIdentity isometryDegrees of freedom
7 related topics

Disk model motions

LobachevskyPoincaré disc modelHyperbolic geometrySU(1,1)
4 related topics

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Motions on the hyperbolic plane

Introduction of metric in the Poincaré half-plane model

Disk model motions

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Hyperbolic motion

Nodes52
Edges51
Triples33
Avg. degree1.96
Density0.038462
Components1

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Hyperbolic motion

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related to References · 20
Hyperbolic motion → American Mathematical Society, Chapter, Geometry, Hyperbolic Motions, ISBN, Lars Ahlfors, Lobachevskian Geometry, Low-dimensional, Mathematical Monographs, Mir Publishers, Moscow, Nagoya Mathematical Journal, Prasolov, Project EuclidFrancis Bonahon, Smogorzhevsky, Student Mathematical Library, The Hyperbolic Plane, Translations, Victor, VM Tikhomirov
related to Use of semi-circle Z · 8
Hyperbolic motion → Any, Consider, Now, Set, Since, So, Suppose, Thus
related to Introduction of metric in the Poincaré half-plane model · 5
Hyperbolic motion → Cartesian, HP, Let, Poincaré, The

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Important terminology

hyperbolic motions geometry reflections two plane line lines absolute degrees freedom model point disk three points complex mappings group half-plane

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hyperbolic motionrelated to Introduction of metric in the Poincaré half-plane modelThe0.60section
Hyperbolic motionrelated to Introduction of metric in the Poincaré half-plane modelPoincaré0.60section
Hyperbolic motionrelated to Introduction of metric in the Poincaré half-plane modelHP0.60section
Hyperbolic motionrelated to Introduction of metric in the Poincaré half-plane modelCartesian0.60section
Hyperbolic motionrelated to Introduction of metric in the Poincaré half-plane modelLet0.60section
Hyperbolic motionrelated to ReferencesLars Ahlfors0.60section
Hyperbolic motionrelated to ReferencesHyperbolic Motions0.60section
Hyperbolic motionrelated to ReferencesNagoya Mathematical Journal0.60section
Hyperbolic motionrelated to ReferencesProject EuclidFrancis Bonahon0.60section
Hyperbolic motionrelated to ReferencesLow-dimensional0.60section
Hyperbolic motionrelated to ReferencesChapter0.60section
Hyperbolic motionrelated to ReferencesThe Hyperbolic Plane0.60section

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