## Title data

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

**Constructing 7-clusters.**

Bayreuth
,
2014
. - 15 p.

## Related URLs

## Abstract in another language

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.

## Further data

Item Type: | Preprint, postprint, working paper, discussion paper |
---|---|

Additional notes: | erscheint in: Serdica Journal of Computing |

Keywords: | Erdös problems; integral point sets; Heron triangles; exhaustive enumeration |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 29 Nov 2014 22:00 |

Last Modified: | 14 Mar 2019 15:41 |

URI: | https://eref.uni-bayreuth.de/id/eprint/4471 |