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.

This is joint work with Pavlo Pylyavskyy [arXiv:2305.07728]. The same material was presented last week at the undergraduate Math Club, and in a Math 668 lecture in December.