
The Plaid Model
Richard Evan Schwartz(Author)
Princeton University Press
Will be published approx. on 19. February 2019
Book
Hardback
280 pages
978-0-691-18137-0 (ISBN)
Description
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.
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.
Reviews / Votes
"[An] enjoyable excursion into a new field."---Meghan De Witt, MAA ReviewsMore details
Series
Language
English
Place of publication
New Jersey
United States
Target group
College/higher education
Professional and scholarly
Product notice
Trade binding
Illustrations
103 b/w illus.
Dimensions
Height: 236 mm
Width: 163 mm
Thickness: 25 mm
Weight
590 gr
ISBN-13
978-0-691-18137-0 (9780691181370)
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Schweitzer Classification
Other editions
Additional editions

E-Book
01/2019
1st Edition
Princeton University Press
€90.99
Available for download
Person
Richard Evan Schwartz is the Chancellor's Professor of Mathematics at Brown University. He is the author of Spherical CR Geometry and Dehn Surgery and Outer Billiards on Kites (both Princeton).