# Constructing 7-Clusters

Kurz, Sascha; Noll, Landon Curt; Rathbun, Randall; Simmons, Chuck

Serdica Journal of Computing (2014)

- Volume: 8, Issue: 1, page 47-70
- ISSN: 1312-6555

## Access Full Article

top## Abstract

top## How to cite

topKurz, Sascha, et al. "Constructing 7-Clusters." Serdica Journal of Computing 8.1 (2014): 47-70. <http://eudml.org/doc/268675>.

@article{Kurz2014,

abstract = {ACM Computing Classification System (1998): G.2, G.4.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.},

author = {Kurz, Sascha, Noll, Landon Curt, Rathbun, Randall, Simmons, Chuck},

journal = {Serdica Journal of Computing},

keywords = {Erdos Problems; Integral Point Sets; Heron Triangles; Exhaustive Enumeration},

language = {eng},

number = {1},

pages = {47-70},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Constructing 7-Clusters},

url = {http://eudml.org/doc/268675},

volume = {8},

year = {2014},

}

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

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 8

IS - 1

SP - 47

EP - 70

AB - ACM Computing Classification System (1998): G.2, G.4.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.

LA - eng

KW - Erdos Problems; Integral Point Sets; Heron Triangles; Exhaustive Enumeration

UR - http://eudml.org/doc/268675

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.