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- Dehn_plane abstract "In geometry, Dehn introduced two examples of planes, a semi-Euclidean geometry and a non-Legendrian geometry, that have infinitely many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle is at least π. A similar phenomenon occurs in hyperbolic geometry, except that the sum of the angles of a triangle is less than π. Dehn's examples use a non-Archimedean field, so that the Archimedean axiom is violated. They were introduced by Max Dehn (1900) and discussed by Hilbert (1902, p.127–130, or p. 42-43 in some later editions).".
- Dehn_plane wikiPageExternalLink 17384-pdf.pdf.
- Dehn_plane wikiPageExternalLink books?id=vEbWAAAAMAAJ&pg=PA404.
- Dehn_plane wikiPageID "4207234".
- Dehn_plane wikiPageLength "4173".
- Dehn_plane wikiPageOutDegree "13".
- Dehn_plane wikiPageRevisionID "646153535".
- Dehn_plane wikiPageWikiLink Archimedean_axiom.
- Dehn_plane wikiPageWikiLink Archimedean_property.
- Dehn_plane wikiPageWikiLink Category:Geometry.
- Dehn_plane wikiPageWikiLink Category:Non-Euclidean_geometry.
- Dehn_plane wikiPageWikiLink Elliptic_geometry.
- Dehn_plane wikiPageWikiLink Euclidean_geometry.
- Dehn_plane wikiPageWikiLink Geometry.
- Dehn_plane wikiPageWikiLink Hyperbolic_geometry.
- Dehn_plane wikiPageWikiLink Mathematische_Annalen.
- Dehn_plane wikiPageWikiLink Metric_(mathematics).
- Dehn_plane wikiPageWikiLink Pythagorean_closure.
- Dehn_plane wikiPageWikiLink Pythagorean_field.
- Dehn_plane wikiPageWikiLink Saccheri–Legendre_theorem.
- Dehn_plane wikiPageWikiLinkText "Dehn plane".
- Dehn_plane authorlink "Max Dehn".
- Dehn_plane first "Max".
- Dehn_plane hasPhotoCollection Dehn_plane.
- Dehn_plane last "Dehn".
- Dehn_plane wikiPageUsesTemplate Template:Citation.
- Dehn_plane wikiPageUsesTemplate Template:Harvs.
- Dehn_plane wikiPageUsesTemplate Template:Harvtxt.
- Dehn_plane year "1900".
- Dehn_plane subject Category:Geometry.
- Dehn_plane subject Category:Non-Euclidean_geometry.
- Dehn_plane comment "In geometry, Dehn introduced two examples of planes, a semi-Euclidean geometry and a non-Legendrian geometry, that have infinitely many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle is at least π. A similar phenomenon occurs in hyperbolic geometry, except that the sum of the angles of a triangle is less than π. Dehn's examples use a non-Archimedean field, so that the Archimedean axiom is violated.".
- Dehn_plane label "Dehn plane".
- Dehn_plane sameAs m.0bp_k2.
- Dehn_plane sameAs Q5252319.
- Dehn_plane sameAs Q5252319.
- Dehn_plane wasDerivedFrom Dehn_plane?oldid=646153535.
- Dehn_plane isPrimaryTopicOf Dehn_plane.