## Title data

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

**Constructing 7-clusters.**

*In:* Serdica Journal of Computing.
Vol. 8
(2014)
Issue 1
.
- pp. 47-70.

ISSN 1312-6555

## 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: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | integral point sets; heron triangles |

Institutions of the University: | 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 |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 23 Apr 2015 12:41 |

Last Modified: | 23 Apr 2015 12:41 |

URI: | https://eref.uni-bayreuth.de/id/eprint/10648 |