2023/05/12 by Sergey Fomin, Fomin, Sergey, Pavlo Pylyavskyy +1 · 3 citations
Engineering · Mathematics · #05E14 #14N20 #51A20 #51M15 #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.07728
openalex publication_date 2023/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary tiling of a closed oriented surface by quadrilateral tiles. This yields a general mechanism for producing new incidence theorems and generalizing the known ones.