|
gptkbp:instanceOf
|
gptkb:logic
noncommutative geometry
|
|
gptkbp:contrastsWith
|
gptkb:Euclidean_geometry
gptkb:elliptic_geometry
|
|
gptkbp:developedBy
|
gptkb:Carl_Friedrich_Gauss
gptkb:János_Bolyai
gptkb:Nikolai_Lobachevsky
|
|
gptkbp:dimensions
|
2
n
|
|
gptkbp:feature
|
parallel postulate does not hold
through a point not on a line, there are infinitely many lines parallel to the given line
|
|
gptkbp:fieldOfStudy
|
gptkb:mathematics
|
|
gptkbp:firstPublished
|
19th century
|
|
gptkbp:hasAxiom
|
parallel postulate replaced
|
|
gptkbp:hasCurvature
|
negative
|
|
gptkbp:hasModel
|
gptkb:Klein_model
gptkb:Poincaré_disk_model
gptkb:Poincaré_half-plane_model
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
hyperbolic geometry
|
|
gptkbp:namedAfter
|
gptkb:hyperbola
|
|
gptkbp:property
|
angle sum of triangle is less than 180 degrees
area of triangle depends on angle sum
|
|
gptkbp:relatedTo
|
gptkb:Riemannian_geometry
gptkb:Teichmüller_theory
gptkb:Fuchsian_groups
|
|
gptkbp:usedIn
|
gptkb:theory_of_relativity
gptkb:topology
gptkb:hyperbolic_manifolds
complex analysis
tessellations
|
|
gptkbp:bfsParent
|
gptkb:Maryam_Mirzakhani
gptkb:Trinity
gptkb:Curtis_T._McMullen
|
|
gptkbp:bfsLayer
|
4
|