2019/10/31 by Jack Hirsch, Kevin Li, Jackson Petty +1
Mathematics · #Algebraic geometry #Combinatorics #Conjecture #Euclidean geometry #Geography #Geometric and Algebraic Topology #Geometry #Hyperbolic geometry #Hyperbolic triangle #Isoperimetric dimension #Isoperimetric inequality #Mathematics #Mathematics and Applications #Perimeter #Plane (geometry) #Point processes and geometric inequalities #Tile #math.MG
paper · pdf · doi:10.1007/s10711-021-00605-2
published as Geom Dedicata, 214 (2021), 65--77 · 13 pages, 2 figures; added arXiv link to November paper
arxiv created 2019/11/15 · openalex publication_date 2021/02/20 · arxiv updated 2022/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular k-gonal tile with 120-degree angles is isoperimetric for its area. We prove his conjecture and more.