Kurz, Sascha ; Noll, Landon Curt ; Rathbun, Randall ; Simmons, Chuck:
Bayreuth , 2014 . - 15 S.
7-cluster_sjc.pdf - Preprint
Available under License Deutsches Urheberrechtsgesetz .
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.