Incidences and tilings
Combinatorics
2023-08-07 v2 Metric Geometry
Abstract
We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\"obius, 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.
Cite
@article{arxiv.2305.07728,
title = {Incidences and tilings},
author = {Sergey Fomin and Pavlo Pylyavskyy},
journal= {arXiv preprint arXiv:2305.07728},
year = {2023}
}
Comments
83 pages, 97 figures. Major revision. New material in Sections 1-2 and 5-8. In particular, Section 7 has been substantially expanded