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The Plaid Model

(AMS-198). Annals of Mathematics Studies

By (author) Richard Evan Schwartz
Format: Paperback / softback
Publisher: Princeton University Press, New Jersey, United States
Published: 19th Feb 2019
Dimensions: w 155mm h 235mm
ISBN-10: 0691181381
ISBN-13: 9780691181387
Barcode No: 9780691181387
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Synopsis
Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites. Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.

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"[An] enjoyable excursion into a new field."---Meghan De Witt, MAA Reviews