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- Hyperbolic_geometry abstract "In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two-dimensional space, for any given line R and point P not on R, there is exactly one line through P that does not intersect R; i.e., that is parallel to R. In hyperbolic geometry there are at least two distinct lines through P which do not intersect R, so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid.Because there is no precise hyperbolic analogue to Euclidean parallel lines, the hyperbolic use of parallel and related terms varies among writers. In this article, the two limiting lines are called asymptotic and lines sharing a common perpendicular are called ultraparallel; the simple word parallel may apply to both.A characteristic property of hyperbolic geometry is that the angles of a triangle add to less than a straight angle, or 180°. In the limit, as the side lengths approach infinity, there are even ideal hyperbolic triangles in which all three angles are 0°.".
- Hyperbolic_geometry thumbnail Hyperbolic.svg?width=300.
- Hyperbolic_geometry wikiPageExternalLink 0903.3287.
- Hyperbolic_geometry wikiPageExternalLink 1012.0880.
- Hyperbolic_geometry wikiPageExternalLink books?id=ZQjBXxxQsucC.
- Hyperbolic_geometry wikiPageExternalLink NonEuclid.html.
- Hyperbolic_geometry wikiPageExternalLink index.php?show=clanak&id_clanak_jezik=114391.
- Hyperbolic_geometry wikiPageExternalLink LW436.jpg.
- Hyperbolic_geometry wikiPageExternalLink 1183548588.
- Hyperbolic_geometry wikiPageExternalLink hyperbolic.
- Hyperbolic_geometry wikiPageExternalLink cannon.pdf.
- Hyperbolic_geometry wikiPageExternalLink HyperbolicTesselations.
- Hyperbolic_geometry wikiPageExternalLink watch?v=B16YjC9OS0k&mode=user&search=.
- Hyperbolic_geometry wikiPageID "241291".
- Hyperbolic_geometry wikiPageRevisionID "603123839".
- Hyperbolic_geometry hasPhotoCollection Hyperbolic_geometry.
- Hyperbolic_geometry id "p/l060030".
- Hyperbolic_geometry title "Gauss–Bolyai–Lobachevsky Space".
- Hyperbolic_geometry title "Hyperbolic Geometry".
- Hyperbolic_geometry title "Lobachevskii geometry".
- Hyperbolic_geometry urlname "Gauss-Bolyai-LobachevskySpace".
- Hyperbolic_geometry urlname "HyperbolicGeometry".
- Hyperbolic_geometry subject Category:Hyperbolic_geometry.
- Hyperbolic_geometry comment "In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two-dimensional space, for any given line R and point P not on R, there is exactly one line through P that does not intersect R; i.e., that is parallel to R.".
- Hyperbolic_geometry label "Geometria hiperboliczna".
- Hyperbolic_geometry label "Geometria hiperbólica".
- Hyperbolic_geometry label "Geometria iperbolica".
- Hyperbolic_geometry label "Geometría hiperbólica".
- Hyperbolic_geometry label "Géométrie hyperbolique".
- Hyperbolic_geometry label "Hyperbolic geometry".
- Hyperbolic_geometry label "Hyperbolische Geometrie".
- Hyperbolic_geometry label "Hyperbolische meetkunde".
- Hyperbolic_geometry label "Геометрия Лобачевского".
- Hyperbolic_geometry label "هندسة زائدية".
- Hyperbolic_geometry label "双曲几何".
- Hyperbolic_geometry label "双曲幾何学".
- Hyperbolic_geometry sameAs Hyperbolická_geometrie.
- Hyperbolic_geometry sameAs Hyperbolische_Geometrie.
- Hyperbolic_geometry sameAs Υπερβολική_γεωμετρία.
- Hyperbolic_geometry sameAs Geometría_hiperbólica.
- Hyperbolic_geometry sameAs Géométrie_hyperbolique.
- Hyperbolic_geometry sameAs Geometria_iperbolica.
- Hyperbolic_geometry sameAs 双曲幾何学.
- Hyperbolic_geometry sameAs 쌍곡_기하학.
- Hyperbolic_geometry sameAs Hyperbolische_meetkunde.
- Hyperbolic_geometry sameAs Geometria_hiperboliczna.
- Hyperbolic_geometry sameAs Geometria_hiperbólica.
- Hyperbolic_geometry sameAs m.01k06b.
- Hyperbolic_geometry sameAs Q209306.
- Hyperbolic_geometry sameAs Q209306.
- Hyperbolic_geometry wasDerivedFrom Hyperbolic_geometry?oldid=603123839.
- Hyperbolic_geometry depiction Hyperbolic.svg.
- Hyperbolic_geometry isPrimaryTopicOf Hyperbolic_geometry.
