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- Sylvester%E2%80%93Gallai_theorem abstract "The Sylvester–Gallai theorem asserts that given a finite number of points in the Euclidean plane, either all the points are collinear; or there is a line which contains exactly two of the points.This claim was posed as a problem by J. J. Sylvester (1893). Kelly (1986) suggests that Sylvester may have been motivated by a related phenomenon in algebraic geometry, in which the inflection points of a cubic curve in the complex projective plane form a configuration of nine points and twelve lines in which each line determined by two of the points contains a third point. The Sylvester–Gallai theorem implies that it is impossible for all nine of these points to have real coordinates. Woodall (1893) claimed to have a short proof, but it was already noted to be incomplete at the time of publication. Eberhard Melchior (1941) proved the projective dual of this theorem, (actually, of a slightly stronger result). Unaware of Melchior's proof, Paul Erdős (1943) again stated the conjecture, which was proved first by Tibor Gallai, and soon afterwards by other authors.A line that contains exactly two of a set of points is known as an ordinary line. There is an algorithm that finds an ordinary line in a set of n points in time proportional to n log n in the worst case.".
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink v=onepage&q=%2211851%22%20woodall&f=false.
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink 03a4.pdf.
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink sylvester1.html.
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink 1257862037.
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink p210.
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink gf4.pdf.
- Sylvester%E2%80%93Gallai_theorem wikiPageExternalLink 1948-01.pdf.
- Sylvester%E2%80%93Gallai_theorem wikiPageID "1052632".
- Sylvester%E2%80%93Gallai_theorem wikiPageRevisionID "639988685".
- Sylvester%E2%80%93Gallai_theorem author1Link "Nicolaas Govert de Bruijn".
- Sylvester%E2%80%93Gallai_theorem author2Link "Paul Erdős".
- Sylvester%E2%80%93Gallai_theorem authorlink "Eberhard Melchior".
- Sylvester%E2%80%93Gallai_theorem authorlink "Gabriel Andrew Dirac".
- Sylvester%E2%80%93Gallai_theorem authorlink "Harold Scott MacDonald Coxeter".
- Sylvester%E2%80%93Gallai_theorem authorlink "James Joseph Sylvester".
- Sylvester%E2%80%93Gallai_theorem authorlink "Paul Erdős".
- Sylvester%E2%80%93Gallai_theorem authorlink "Theodore Motzkin".
- Sylvester%E2%80%93Gallai_theorem first "Eberhard".
- Sylvester%E2%80%93Gallai_theorem first "Gabriel".
- Sylvester%E2%80%93Gallai_theorem first "H. S. M.".
- Sylvester%E2%80%93Gallai_theorem first "J. J.".
- Sylvester%E2%80%93Gallai_theorem first "Paul".
- Sylvester%E2%80%93Gallai_theorem first "Theodore".
- Sylvester%E2%80%93Gallai_theorem hasPhotoCollection Sylvester–Gallai_theorem.
- Sylvester%E2%80%93Gallai_theorem last "Coxeter".
- Sylvester%E2%80%93Gallai_theorem last "Dirac".
- Sylvester%E2%80%93Gallai_theorem last "Erdős".
- Sylvester%E2%80%93Gallai_theorem last "Melchior".
- Sylvester%E2%80%93Gallai_theorem last "Motzkin".
- Sylvester%E2%80%93Gallai_theorem last "Sylvester".
- Sylvester%E2%80%93Gallai_theorem last "de Bruijn".
- Sylvester%E2%80%93Gallai_theorem title "Ordinary Line".
- Sylvester%E2%80%93Gallai_theorem urlname "OrdinaryLine".
- Sylvester%E2%80%93Gallai_theorem year "1893".
- Sylvester%E2%80%93Gallai_theorem year "1941".
- Sylvester%E2%80%93Gallai_theorem year "1943".
- Sylvester%E2%80%93Gallai_theorem year "1948".
- Sylvester%E2%80%93Gallai_theorem year "1951".
- Sylvester%E2%80%93Gallai_theorem year "1969".
- Sylvester%E2%80%93Gallai_theorem subject Category:Articles_containing_proofs.
- Sylvester%E2%80%93Gallai_theorem subject Category:Euclidean_plane_geometry.
- Sylvester%E2%80%93Gallai_theorem subject Category:Matroid_theory.
- Sylvester%E2%80%93Gallai_theorem subject Category:Theorems_in_discrete_geometry.
- Sylvester%E2%80%93Gallai_theorem type Abstraction100002137.
- Sylvester%E2%80%93Gallai_theorem type Communication100033020.
- Sylvester%E2%80%93Gallai_theorem type Message106598915.
- Sylvester%E2%80%93Gallai_theorem type Proposition106750804.
- Sylvester%E2%80%93Gallai_theorem type Statement106722453.
- Sylvester%E2%80%93Gallai_theorem type Theorem106752293.
- Sylvester%E2%80%93Gallai_theorem type TheoremsInDiscreteGeometry.
- Sylvester%E2%80%93Gallai_theorem comment "The Sylvester–Gallai theorem asserts that given a finite number of points in the Euclidean plane, either all the points are collinear; or there is a line which contains exactly two of the points.This claim was posed as a problem by J. J. Sylvester (1893).".
- Sylvester%E2%80%93Gallai_theorem label "Satz von Sylvester-Gallai".
- Sylvester%E2%80%93Gallai_theorem label "Sylvester–Gallai theorem".
- Sylvester%E2%80%93Gallai_theorem label "Sylvester–Gallai-tétel".
- Sylvester%E2%80%93Gallai_theorem label "Teorema de Sylvester-Gallai".
- Sylvester%E2%80%93Gallai_theorem label "Teorema de Sylvester–Gallai".
- Sylvester%E2%80%93Gallai_theorem label "Teorema di Sylvester-Gallai".
- Sylvester%E2%80%93Gallai_theorem label "Théorème de Sylvester-Gallai".
- Sylvester%E2%80%93Gallai_theorem label "Теорема Сильвестра".
- Sylvester%E2%80%93Gallai_theorem sameAs m.041vf8.
- Sylvester%E2%80%93Gallai_theorem sameAs Sylvester–Gallai_theorem.
- Sylvester%E2%80%93Gallai_theorem wasDerivedFrom Sylvester–Gallai_theorem?oldid=639988685.
- Sylvester%E2%80%93Gallai_theorem isPrimaryTopicOf Sylvester–Gallai_theorem.