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Title data
Kurz, Sascha ; Noll, Landon Curt ; Rathbun, Randall ; Simmons, Chuck:
Constructing 7-clusters.
Bayreuth
,
2014
. - 15 S.
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Abstract
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 |
|---|---|
| Additional notes (visible to public): | erschienen in:
Serdica Journal of Computing. Bd. 8 (2014) Heft 1 . - S. 47-70. |
| Keywords: | Erdös problems; integral point sets; Heron triangles; exhaustive enumeration |
| DDC Subjects: | 500 Science > 510 Mathematics |
| 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 Mathematical Economics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-1786-0 |
| Date Deposited: | 24 Nov 2014 09:57 |
| Last Modified: | 06 Oct 2025 12:47 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/1786 |
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