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A186704 The minimum number of distinct distances determined by n points in the Euclidean plane. 1


%S 0,1,1,2,2,3,3,4,4,5,5,5,6

%N The minimum number of distinct distances determined by n points in the Euclidean plane.

%C The Mathoverflow link has an image from page 200 of Brass reference.

%D P. Brass, W. O. J. Moser and J. Pach, Research Problems in Discrete Geometry, Springer (2005), p. 200.

%H P. Erdős and P. Fishburn, <a href="https://doi.org/10.1016/0012-365X(95)00153-N">Maximum planar sets that determine k distances</a>, Discrete Math. 160 (1996), 115-125.

%H L. Guth, N. H. Katz, <a href="http://arxiv.org/abs/1011.4105">On the Erdős distinct distance problem in the plane</a>, arXiv:1011.4105 [math.CO], 2010-2011.

%H R. Mansuy, <a href="http://www.ihp.fr/fr/seminaire/mathpark-programme">Le problème des distances d'Erdős</a>, Mathematik Park, Institut Henri Poincaré, Paris, 2013.

%H Mathoverflow, <a href="http://mathoverflow.net/questions/58203/">Erdos distance problem n=12</a>

%H K. Schade, <a href="http://www.wm.uni-bayreuth.de/fileadmin/Sacha/Lehre/SoftwarePraktika/doc_schade.pdf">Softwarepraktikum, Sommersemester 2007</a>

%e a(4) = a(5) = 2 from the 2 distinct distances between vertices of a square and a regular pentagon.

%K nonn,hard,nice

%O 1,4

%A _Michael Somos_, Feb 25 2011

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Last modified May 11 02:34 EDT 2021. Contains 343784 sequences. (Running on oeis4.)