Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2429

 Title: Constructing 7-Clusters Authors: Kurz, SaschaNoll, Landon CurtRathbun, RandallSimmons, Chuck Keywords: Erdos ProblemsIntegral Point SetsHeron TrianglesExhaustive Enumeration Issue Date: 2014 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Journal of Computing, Vol. 8, No 1, (2014), 47p-70p Abstract: A set of n lattice points in the plane, no three on a line and no four on a circle, such that all pairwise distances and coordinates are integers is called an n-cluster (in R^2). We determine the smallest 7-cluster with respect to its diameter. Additionally we provide a toolbox of algorithms which allowed us to computationally locate over 1000 different 7-clusters, some of them having huge integer edge lengths. Along the way, we have exhaustively determined all Heronian triangles with largest edge length up to 6 · 10^6. Description: ACM Computing Classification System (1998): G.2, G.4. URI: http://hdl.handle.net/10525/2429 ISSN: 1312-6555 Appears in Collections: Volume 8 Number 1

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