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- Playfairs_axiom abstract "In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate):In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry and was named after the Scottish mathematician John Playfair. The "at most" clause is all that is needed since it can be proved from the remaining axioms that at least one parallel line exists. The statement is often written with the phrase, "there is one and only one parallel". In Euclid's Elements, two lines are said to be parallel if they never meet and other characterizations of parallel lines are not used.This axiom is used not only in Euclidean geometry but also in the broader study of affine geometry where the concept of parallelism is central. In the affine geometry setting, the stronger form of Playfair's axiom (where "at most" is replaced by "one and only one") is needed since the axioms of neutral geometry are not present to provide a proof of existence. Playfair's version of the axiom has become so popular that it is often referred to as Euclid's parallel axiom, even though it was not Euclid's version of the axiom.".
- Playfairs_axiom thumbnail Point_and_line.png?width=300.
- Playfairs_axiom wikiPageID "33731592".
- Playfairs_axiom wikiPageLength "9960".
- Playfairs_axiom wikiPageOutDegree "39".
- Playfairs_axiom wikiPageRevisionID "681898631".
- Playfairs_axiom wikiPageWikiLink Absolute_geometry.
- Playfairs_axiom wikiPageWikiLink Affine_geometry.
- Playfairs_axiom wikiPageWikiLink Arthur_Cayley.
- Playfairs_axiom wikiPageWikiLink Augustus_De_Morgan.
- Playfairs_axiom wikiPageWikiLink Axiom.
- Playfairs_axiom wikiPageWikiLink Binary_relation.
- Playfairs_axiom wikiPageWikiLink British_Association.
- Playfairs_axiom wikiPageWikiLink British_Science_Association.
- Playfairs_axiom wikiPageWikiLink Category:Foundations_of_geometry.
- Playfairs_axiom wikiPageWikiLink David_Hilbert.
- Playfairs_axiom wikiPageWikiLink Dover_Publications.
- Playfairs_axiom wikiPageWikiLink Elliptic_geometry.
- Playfairs_axiom wikiPageWikiLink Elliptical_geometry.
- Playfairs_axiom wikiPageWikiLink Equivalence_relation.
- Playfairs_axiom wikiPageWikiLink Euclid.
- Playfairs_axiom wikiPageWikiLink Euclidean_geometry.
- Playfairs_axiom wikiPageWikiLink Euclids_Elements.
- Playfairs_axiom wikiPageWikiLink Geometry.
- Playfairs_axiom wikiPageWikiLink Hilberts_axioms.
- Playfairs_axiom wikiPageWikiLink John_Playfair.
- Playfairs_axiom wikiPageWikiLink Line_(geometry).
- Playfairs_axiom wikiPageWikiLink Line_(mathematics).
- Playfairs_axiom wikiPageWikiLink Line_segment.
- Playfairs_axiom wikiPageWikiLink Logical_equivalence.
- Playfairs_axiom wikiPageWikiLink Logically_equivalent.
- Playfairs_axiom wikiPageWikiLink Mathematician.
- Playfairs_axiom wikiPageWikiLink Parallel_(geometry).
- Playfairs_axiom wikiPageWikiLink Parallel_lines.
- Playfairs_axiom wikiPageWikiLink Parallel_postulate.
- Playfairs_axiom wikiPageWikiLink Proclus.
- Playfairs_axiom wikiPageWikiLink Right_angle.
- Playfairs_axiom wikiPageWikiLink Spherical_geometry.
- Playfairs_axiom wikiPageWikiLink T._L._Heath.
- Playfairs_axiom wikiPageWikiLink Thomas_Little_Heath.
- Playfairs_axiom wikiPageWikiLink Transitive_relation.
- Playfairs_axiom wikiPageWikiLink Transposition_(logic).
- Playfairs_axiom wikiPageWikiLink William_Ludlam.
- Playfairs_axiom wikiPageWikiLink File:Parallel_postulate_en.svg.
- Playfairs_axiom wikiPageWikiLink File:Point_and_line.png.
- Playfairs_axiom wikiPageWikiLink File:Two_Parallel_lines.svg.
- Playfairs_axiom wikiPageWikiLinkText "Playfair's axiom".
- Playfairs_axiom wikiPageWikiLinkText "Playfair's form".
- Playfairs_axiom hasPhotoCollection Playfairs_axiom.
- Playfairs_axiom wikiPageUsesTemplate Template:Citation.
- Playfairs_axiom wikiPageUsesTemplate Template:Cite_book.
- Playfairs_axiom wikiPageUsesTemplate Template:Reflist.
- Playfairs_axiom subject Category:Foundations_of_geometry.
- Playfairs_axiom hypernym Axiom.
- Playfairs_axiom comment "In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate):In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry and was named after the Scottish mathematician John Playfair.".
- Playfairs_axiom label "Playfair's axiom".
- Playfairs_axiom sameAs مسلمة_بلاي_فير.
- Playfairs_axiom sameAs اصل_توازی_هیلبرت.
- Playfairs_axiom sameAs Assiòma_ëd_Playfair.
- Playfairs_axiom sameAs m.0ds5q87.
- Playfairs_axiom sameAs Q3915714.
- Playfairs_axiom sameAs Q3915714.
- Playfairs_axiom sameAs 普莱费尔公理.
- Playfairs_axiom wasDerivedFrom Playfairs_axiomoldid=681898631.
- Playfairs_axiom depiction Point_and_line.png.
- Playfairs_axiom isPrimaryTopicOf Playfairs_axiom.