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gptkbp:instanceOf
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gptkb:mathematical_concept
Non-Euclidean geometry
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gptkbp:application
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gptkb:Topology
gptkb:Theoretical_physics
gptkb:Relativity_theory
Complex analysis
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gptkbp:contrastsWith
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gptkb:Euclidean_geometry
gptkb:Elliptic_geometry
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gptkbp:developedBy
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gptkb:Carl_Friedrich_Gauss
gptkb:János_Bolyai
gptkb:Nikolai_Lobachevsky
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gptkbp:dimensions
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n-dimensional
2-dimensional
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gptkbp:feature
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Multiple parallel lines through a point
Negative curvature
Parallel postulate does not hold
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gptkbp:field
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gptkb:Mathematics
|
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gptkbp:hasAxiom
|
Through a point not on a line, there are infinitely many lines parallel to the given line
|
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gptkbp:hasModel
|
gptkb:Klein_model
gptkb:Poincaré_disk_model
gptkb:Poincaré_half-plane_model
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Hyperbolic geometry
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gptkbp:influenced
|
gptkb:logic
gptkb:Modern_geometry
Cosmology
|
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gptkbp:property
|
Angle sum of triangle less than 180 degrees
Area of triangle depends on angle sum
No similar but non-congruent triangles
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gptkbp:relatedTo
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gptkb:Riemannian_geometry
gptkb:Hyperbolic_space
|
|
gptkbp:studiedIn
|
19th century
|
|
gptkbp:bfsParent
|
gptkb:Thurston's_eight_geometries
gptkb:Parallel_postulate
gptkb:Tanh
gptkb:Teichmüller_metric
gptkb:Dilogarithm
|
|
gptkbp:bfsLayer
|
6
|