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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:category
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gptkb:mathematics
|
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gptkbp:contrastsWith
|
gptkb:Euclidean_geometry
|
|
gptkbp:developedBy
|
gptkb:Carl_Friedrich_Gauss
gptkb:János_Bolyai
gptkb:Nikolai_Lobachevsky
gptkb:Bernhard_Riemann
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gptkbp:field
|
gptkb:geometry
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gptkbp:hasApplication
|
gptkb:navigation
cartography
computer graphics
physics
|
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gptkbp:hasAxiom
|
negation of the parallel postulate
|
|
gptkbp:hasConcept
|
geodesics
parallel lines
angle sum of triangle
curved space
|
|
gptkbp:hasProperty
|
angle sum of triangle not equal to 180 degrees
no parallel lines (elliptic)
space of constant curvature
multiple lines through a point not intersecting a given line (hyperbolic)
|
|
gptkbp:hasSubfield
|
gptkb:geometry
gptkb:elliptic_geometry
gptkb:hyperbolic_geometry
gptkb:spherical_geometry
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Non-Euclidean Geometry
|
|
gptkbp:includes
|
gptkb:elliptic_geometry
gptkb:hyperbolic_geometry
|
|
gptkbp:influencedBy
|
gptkb:logic
gptkb:Euclid's_fifth_postulate
differential geometry
modern physics
|
|
gptkbp:language
|
gptkb:mathematics
|
|
gptkbp:originatedIn
|
19th century
|
|
gptkbp:relatedTo
|
gptkb:Klein_model
gptkb:Lobachevskian_geometry
gptkb:Beltrami–Klein_model
gptkb:Poincaré_disk_model
gptkb:Riemannian_geometry
gptkb:Poincaré_half-plane_model
|
|
gptkbp:studiedBy
|
gptkb:mathematician
|
|
gptkbp:studies
|
spaces where the parallel postulate does not hold
|
|
gptkbp:usedIn
|
gptkb:art
gptkb:cosmology
gptkb:general_relativity
gptkb:topology
|
|
gptkbp:bfsParent
|
gptkb:H._S._M._Coxeter
gptkb:H.S.M._Coxeter
|
|
gptkbp:bfsLayer
|
6
|