Beck's Theorem (geometry)
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High Quality Content by WIKIPEDIA articles! In the context of discrete geometry, Beck's theorem may refer to several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck. The two results described below primarily concern lower bounds on the number of lines determined by a set of points in the plane. (Any line containing at least two points of point set is said to be determined by that point set.) The Erd s Beck theorem is a variation of a classical result by L.M. Kelly and W.O.J. Moser involving config...
High Quality Content by WIKIPEDIA articles! In the context of discrete geometry, Beck's theorem may refer to several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck. The two results described below primarily concern lower bounds on the number of lines determined by a set of points in the plane. (Any line containing at least two points of point set is said to be determined by that point set.) The Erd s Beck theorem is a variation of a classical result by L.M. Kelly and W.O.J. Moser involving configurations of n points of which at most n k are collinear, for some 0kn 1. They showed that if n is sufficiently large then the configuration spans at least kn (1/2)(3k+2)(k 1) lines.
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