De Bruijn Erd's Theorem (incidence geometry)
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High Quality Content by WIKIPEDIA articles! In incidence geometry, the De Bruijn Erd s theorem, originally published by Nicolaas Govert de Bruijn and Paul Erd s (1948), states a lower bound on the number of lines determined by n points in a projective plane. By duality, this is also a bound on the number of intersection points determined by a configuration of lines. Although the proof given by De Bruijn and Erd s is combinatorial, De Bruijn and Erd s noted in their paper that the analogous (Euclidean) result is a consequence of the Sylvester Gallai theorem, by an induction on the number of points.…mehr

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High Quality Content by WIKIPEDIA articles! In incidence geometry, the De Bruijn Erd s theorem, originally published by Nicolaas Govert de Bruijn and Paul Erd s (1948), states a lower bound on the number of lines determined by n points in a projective plane. By duality, this is also a bound on the number of intersection points determined by a configuration of lines. Although the proof given by De Bruijn and Erd s is combinatorial, De Bruijn and Erd s noted in their paper that the analogous (Euclidean) result is a consequence of the Sylvester Gallai theorem, by an induction on the number of points.