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- Saccheri–Legendre_theorem abstract "In absolute geometry, the Saccheri–Legendre theorem asserts that the sum of the angles in a triangle is at most 180°. Absolute geometry is the geometry obtained from assuming all the axioms that lead to Euclidean geometry with the exception of the axiom that is equivalent to the parallel postulate of Euclid.The theorem is named after Giovanni Girolamo Saccheri and Adrien-Marie Legendre.The existence of triangle with angle sum of 180 degrees in absolute geometry implies Euclid's parallel postulate. Similarly, the existence of at least one triangle with angle sum of less than 180 degrees implies the characteristic postulate of hyperbolic geometry.Dehn gave an example of a non-Legendrian geometry where the angle sum of a triangle is greater than 180 degrees, and a semi-Euclidean geometry where there is a triangle with an angle sum of 180 degrees but Euclid's parallel postulate fails. In Dehn's geometries the Archimedean axiom does not hold.".
- Saccheri–Legendre_theorem wikiPageID "23413137".
- Saccheri–Legendre_theorem wikiPageLength "1703".
- Saccheri–Legendre_theorem wikiPageOutDegree "16".
- Saccheri–Legendre_theorem wikiPageRevisionID "607214426".
- Saccheri–Legendre_theorem wikiPageWikiLink Absolute_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Adrien-Marie_Legendre.
- Saccheri–Legendre_theorem wikiPageWikiLink Archimedean_axiom.
- Saccheri–Legendre_theorem wikiPageWikiLink Archimedean_property.
- Saccheri–Legendre_theorem wikiPageWikiLink Axiomatic_system.
- Saccheri–Legendre_theorem wikiPageWikiLink Category:Euclidean_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Category:Non-Euclidean_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Category:Theorems_in_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Category:Triangle_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Dehn_plane.
- Saccheri–Legendre_theorem wikiPageWikiLink Euclidean_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Giovanni_Girolamo_Saccheri.
- Saccheri–Legendre_theorem wikiPageWikiLink Hyperbolic_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Max_Dehn.
- Saccheri–Legendre_theorem wikiPageWikiLink Non-Legendrian_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Parallel_postulate.
- Saccheri–Legendre_theorem wikiPageWikiLink Semi-Euclidean_geometry.
- Saccheri–Legendre_theorem wikiPageWikiLink Triangle.
- Saccheri–Legendre_theorem wikiPageWikiLinkText "Legendre angle sum theorem".
- Saccheri–Legendre_theorem wikiPageWikiLinkText "Legendre's theorem".
- Saccheri–Legendre_theorem wikiPageWikiLinkText "Saccheri–Legendre theorem".
- Saccheri–Legendre_theorem hasPhotoCollection Saccheri–Legendre_theorem.
- Saccheri–Legendre_theorem wikiPageUsesTemplate Template:Geometry-stub.
- Saccheri–Legendre_theorem wikiPageUsesTemplate Template:Reflist.
- Saccheri–Legendre_theorem subject Category:Euclidean_geometry.
- Saccheri–Legendre_theorem subject Category:Non-Euclidean_geometry.
- Saccheri–Legendre_theorem subject Category:Theorems_in_geometry.
- Saccheri–Legendre_theorem subject Category:Triangle_geometry.
- Saccheri–Legendre_theorem comment "In absolute geometry, the Saccheri–Legendre theorem asserts that the sum of the angles in a triangle is at most 180°.".
- Saccheri–Legendre_theorem label "Saccheri–Legendre theorem".
- Saccheri–Legendre_theorem sameAs قضیه_ساکری_لوژاندر.
- Saccheri–Legendre_theorem sameAs m.06w8d6f.
- Saccheri–Legendre_theorem sameAs Q7396621.
- Saccheri–Legendre_theorem sameAs Q7396621.
- Saccheri–Legendre_theorem wasDerivedFrom Saccheri–Legendre_theorem?oldid=607214426.
- Saccheri–Legendre_theorem isPrimaryTopicOf Saccheri–Legendre_theorem.