Erdos Problems Integral Point Sets Heron Triangles Exhaustive Enumeration
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 8, No 1, (2014), 47p-70p
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.
ACM Computing Classification System (1998): G.2, G.4.