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Title: Constructing 7-Clusters
Authors: Kurz, Sascha
Noll, Landon Curt
Rathbun, Randall
Simmons, Chuck
Keywords: Erdos Problems
Integral Point Sets
Heron Triangles
Exhaustive 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.
ISSN: 1312-6555
Appears in Collections:Volume 8 Number 1

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