Math 272

** Instructor ** Prof. Rich Schwartz

** When/Where ** Kassar 205, Tu-Th 1-2:20

** summary ** This is a graduate topics class on piecewise isometries. List of Topics:

- general dissection: The Banach-Tarski Paradox.

notes on the B.T. Theorem
- polyhedral dissection: The case of polygons, Pick's Theorem, The Dehn-Sydler Theorem

notes on Dehn's theorem

notes on Dehn-Sydler Theorem

- Quasi-Crystals: Penrose tiling, pentagrids, cut and project method

De Bruijn's papers
- Sturmian Sequences: Continued Fractions, Renormalization

Notes on Continued Fractions

Smillie/Ulcigrai paper

- Outer billiards: General Properties, the regular pentagon, kites, rational polygons

Tabachnikov's paper

My paper on the pinwheel lemma

preprint arXiv version of my book

- Rational Billiards: Hyperbolic geometry, translation surfaces,Veech examples

See chapters 16 and 17 in my other book.