Constructing 7-clusters

Titelangaben

Kurz, Sascha ; Noll, Landon Curt ; Rathbun, Randall ; Simmons, Chuck:
Constructing 7-clusters.
In: Serdica Journal of Computing. Bd. 8 (2014) Heft 1 . - S. 47-70.
ISSN 1312-6555

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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 integral 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. On the way, we have exhaustively determined all Heronian triangles with largest edge length up to 6 millions.