| dbo:abstract |
In absolute geometry, the Saccheri–Legendre theorem states 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 at least one 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. Max 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. (en) 절대기하학에서 사케리-르장드르 정리(영어: Saccheri–Legendre theorem)는 삼각형의 내각합에 대한 정리이다. (ko) |
| dbo:wikiPageID |
23413137 (xsd:integer) |
| dbo:wikiPageLength |
1806 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
986718518 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Non-Legendrian_geometry dbc:Euclidean_geometry dbr:Max_Dehn dbc:Non-Euclidean_geometry dbr:Parallel_postulate dbr:Giovanni_Girolamo_Saccheri dbr:Adrien-Marie_Legendre dbc:Theorems_about_triangles dbr:Hyperbolic_geometry dbr:Absolute_geometry dbr:Triangle dbr:Axiomatic_system dbr:Euclidean_geometry dbr:Archimedean_axiom dbr:Semi-Euclidean_geometry |
| dbp:wikiPageUsesTemplate |
dbt:Geometry-stub dbt:Reflist dbt:Short_description |
| dct:subject |
dbc:Euclidean_geometry dbc:Non-Euclidean_geometry dbc:Theorems_about_triangles |
| rdf:type |
yago:WikicatTheoremsInGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293 |
| rdfs:comment |
절대기하학에서 사케리-르장드르 정리(영어: Saccheri–Legendre theorem)는 삼각형의 내각합에 대한 정리이다. (ko) In absolute geometry, the Saccheri–Legendre theorem states 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. (en) |
| rdfs:label |
사케리-르장드르 정리 (ko) Saccheri–Legendre theorem (en) |
| owl:sameAs |
freebase:Saccheri–Legendre theorem wikidata:Saccheri–Legendre theorem dbpedia-fa:Saccheri–Legendre theorem dbpedia-ko:Saccheri–Legendre theorem https://global.dbpedia.org/id/4upCq |
| prov:wasDerivedFrom |
wikipedia-en:Saccheri–Legendre_theorem?oldid=986718518&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Saccheri–Legendre_theorem |
| is dbo:wikiPageRedirects of |
dbr:Saccheri-Legendre_theorem dbr:Legendre's_theorem dbr:Legendre_theorem |
| is dbo:wikiPageWikiLink of |
dbr:Dehn_plane dbr:Max_Dehn dbr:Giovanni_Girolamo_Saccheri dbr:Adrien-Marie_Legendre dbr:Foundations_of_geometry dbr:Absolute_geometry dbr:Saccheri-Legendre_theorem dbr:List_of_theorems dbr:List_of_things_named_after_Adrien-Marie_Legendre dbr:Legendre's_theorem dbr:Legendre_theorem |
| is foaf:primaryTopic of |
wikipedia-en:Saccheri–Legendre_theorem |