Sylvester Gallai Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Sylvester Gallai theorem asserts that given a finite number of points in the Euclidean plane, eitherThis 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…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Sylvester Gallai theorem asserts that given a finite number of points in the Euclidean plane, eitherThis 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. Eberhard Melchior (1940) proved the projective dual of this theorem, (actually, of a slightly stronger result). Unaware of Melchior''s proof, Paul Erd s (1943) again stated the conjecture, which was proved first by Tibor Gallai, and soon afterwards by other authors.