2025/11/20 by Mahabaduge, Ghaura
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2512.07839
openalex publication_date 2025/11/20 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28
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,√(m))] with m ≡ 3 \pmod4. 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 ≥ N, the lattice Λ(m) contains an equilateral n-gon. This extends previous classifications of equilateral polygons in planar lattices.