Lattice triangles whose centers are lattice points
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914514951208960 |
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| author | Aebi, Christian Cairns, Grant |
| author_facet | Aebi, Christian Cairns, Grant |
| contents | We show that for an integer $\ell$, there exists an acute integer lattice triangle of lattice perimeter $\ell$ such that its orthocenter is an integer lattice point, if and only if $\ell=6 $ or $\ell\ge 8$. Analogous results are obtained for the circumcenter and the centroid, and the results are contrasted with those for obtuse and right triangles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lattice triangles whose centers are lattice points Aebi, Christian Cairns, Grant General Mathematics 52C05, 51M04 We show that for an integer $\ell$, there exists an acute integer lattice triangle of lattice perimeter $\ell$ such that its orthocenter is an integer lattice point, if and only if $\ell=6 $ or $\ell\ge 8$. Analogous results are obtained for the circumcenter and the centroid, and the results are contrasted with those for obtuse and right triangles. |
| title | Lattice triangles whose centers are lattice points |
| topic | General Mathematics 52C05, 51M04 |
| url | https://arxiv.org/abs/2604.25956 |