About: Saccheri–Legendre theorem

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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.

Attributes	Values
rdf:type	yago:WikicatTheoremsInGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	사케리-르장드르 정리 (ko) Saccheri–Legendre theorem (en)
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)
dcterms:subject	Euclidean geometry Non-Euclidean geometry Theorems about triangles
Wikipage page ID	23413137 (xsd:integer)
Wikipage revision ID	986718518 (xsd:integer)
Link from a Wikipage to another Wikipage	Non-Legendrian geometry Euclidean geometry Max Dehn Non-Euclidean geometry Parallel postulate Giovanni Girolamo Saccheri Adrien-Marie Legendre Theorems about triangles Hyperbolic geometry Absolute geometry Triangle Axiomatic system Euclidean geometry Archimedean axiom Semi-Euclidean geometry
sameAs	Saccheri–Legendre theorem Saccheri–Legendre theorem Saccheri–Legendre theorem Saccheri–Legendre theorem Saccheri–Legendre theorem
dbp:wikiPageUsesTemplate	dbt:Geometry-stub dbt:Reflist dbt:Short_description
has 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)
prov:wasDerivedFrom	wikipedia-en:Saccheri–Legendre_theorem?oldid=986718518&ns=0
page length (characters) of wiki page	1806 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Saccheri–Legendre_theorem
is Link from a Wikipage to another Wikipage of	Dehn plane Max Dehn Giovanni Girolamo Saccheri Adrien-Marie Legendre Foundations of geometry Absolute geometry Saccheri-Legendre theorem List of theorems List of things named after Adrien-Marie Legendre Legendre's theorem Legendre theorem
is Wikipage redirect of	Saccheri-Legendre theorem Legendre's theorem Legendre theorem
is foaf:primaryTopic of	wikipedia-en:Saccheri–Legendre_theorem

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