Equilateral n-gons in planar integer lattices
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908699112505344 |
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| author | Mahabaduge, Ghaura |
| author_facet | Mahabaduge, Ghaura |
| contents | We study the existence of equilateral polygons in planar integer lattices. Maehara showed that it's sufficient to work with rectangular lattices $Λ(m) = L[(1,0),(0,\sqrt{m})]$ with $m \equiv 3 \pmod{4}$. Building on results of Maehara and of Iino and Sakiyama, we show that for every such $m$ there exists $N$ such that for all $n \geq N$, the lattice $Λ(m)$ contains an equilateral $n$-gon. This extends previous classifications of equilateral polygons in planar lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilateral n-gons in planar integer lattices Mahabaduge, Ghaura Metric Geometry Combinatorics We study the existence of equilateral polygons in planar integer lattices. Maehara showed that it's sufficient to work with rectangular lattices $Λ(m) = L[(1,0),(0,\sqrt{m})]$ with $m \equiv 3 \pmod{4}$. Building on results of Maehara and of Iino and Sakiyama, we show that for every such $m$ there exists $N$ such that for all $n \geq N$, the lattice $Λ(m)$ contains an equilateral $n$-gon. This extends previous classifications of equilateral polygons in planar lattices. |
| title | Equilateral n-gons in planar integer lattices |
| topic | Metric Geometry Combinatorics |
| url | https://arxiv.org/abs/2512.07839 |