The sad life of lattice triangles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866918359062282240 |
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| author | Aebi, Christian Cairns, Grant |
| author_facet | Aebi, Christian Cairns, Grant |
| contents | This paper treats triangles in the plane whose vertices lie on the integer lattice, i.e., the vertices have integer coordinates. It shows that apart from trivial examples, the circumcenter, centroid and orthocenter of such triangles never all lie on the integer lattice. Several further observations are made concerning the circumcenter, centroid and orthocenter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23392 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The sad life of lattice triangles Aebi, Christian Cairns, Grant Combinatorics 52C05, 51M04 This paper treats triangles in the plane whose vertices lie on the integer lattice, i.e., the vertices have integer coordinates. It shows that apart from trivial examples, the circumcenter, centroid and orthocenter of such triangles never all lie on the integer lattice. Several further observations are made concerning the circumcenter, centroid and orthocenter. |
| title | The sad life of lattice triangles |
| topic | Combinatorics 52C05, 51M04 |
| url | https://arxiv.org/abs/2602.23392 |