Geodesic
Constructing 7-Clusters
Serdica Journal of Computing, Tome 8 (2014) no. 1, pp. 47-70.

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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.
Keywords: Erdos Problems, Integral Point Sets, Heron Triangles, Exhaustive Enumeration 
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Kurz, Sascha; Noll, Landon Curt; Rathbun, Randall; Simmons, Chuck. Constructing 7-Clusters. Serdica Journal of Computing, Tome 8 (2014) no. 1, pp. 47-70. http://geodesic.mathdoc.fr/item/SJC_2014_8_1_a3/