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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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The Plaid Model - (AMS-198) (Paperback)
Loot Price: R1,823
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The Plaid Model - (AMS-198) (Paperback)
Series: Annals of Mathematics Studies
Expected to ship within 12 - 19 working days
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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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