Sergey Fomin, Pavlo Pylyavskyy
Published 2023-05-12Version 1
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.
Comments: 70 pages, 79 figures
Incidences, tilings, and fields
Incidence Theorems and Their Applications
Series expansions for $1/π^m$ and $π^m$
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