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

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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 
@article{SJC_2014_8_1_a3,
     author = {Kurz, Sascha and Noll, Landon Curt and Rathbun, Randall and Simmons, Chuck},
     title = {Constructing {7-Clusters}},
     journal = {Serdica Journal of Computing},
     pages = {47--70},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJC_2014_8_1_a3/}
}
TY  - JOUR
AU  - Kurz, Sascha
AU  - Noll, Landon Curt
AU  - Rathbun, Randall
AU  - Simmons, Chuck
TI  - Constructing 7-Clusters
JO  - Serdica Journal of Computing
PY  - 2014
SP  - 47
EP  - 70
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2014_8_1_a3/
LA  - en
ID  - SJC_2014_8_1_a3
ER  - 
%0 Journal Article
%A Kurz, Sascha
%A Noll, Landon Curt
%A Rathbun, Randall
%A Simmons, Chuck
%T Constructing 7-Clusters
%J Serdica Journal of Computing
%D 2014
%P 47-70
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2014_8_1_a3/
%G en
%F SJC_2014_8_1_a3
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/