The Plaid Model: (AMS-198)
()
About this ebook
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.
Richard Evan Schwartz
Richard Evan Schwartz is professor of mathematics at Brown University and the author of Spherical CR Geometry and Dehn Surgery (Princeton).
Related to The Plaid Model
Titles in the series (100)
Algebraic Theory of Numbers. (AM-1), Volume 1 Rating: 0 out of 5 stars0 ratingsDegree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-22), Volume 2: The Geometry of Orthogonal Spaces. (AM-22) Rating: 0 out of 5 stars0 ratingsThe Calculi of Lambda-Conversion (AM-6), Volume 6 Rating: 4 out of 5 stars4/5Consistency of the Continuum Hypothesis. (AM-3), Volume 3 Rating: 0 out of 5 stars0 ratingsFinite Dimensional Vector Spaces. (AM-7), Volume 7 Rating: 4 out of 5 stars4/5Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) Rating: 0 out of 5 stars0 ratingsTranscendental Numbers. (AM-16) Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-28), Volume II Rating: 0 out of 5 stars0 ratingsExistence Theorems in Partial Differential Equations. (AM-23), Volume 23 Rating: 0 out of 5 stars0 ratingsCurvature and Betti Numbers. (AM-32), Volume 32 Rating: 0 out of 5 stars0 ratingsIsoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27 Rating: 0 out of 5 stars0 ratingsTopics in Topology. (AM-10), Volume 10 Rating: 0 out of 5 stars0 ratingsIntroduction to Non-Linear Mechanics. (AM-11), Volume 11 Rating: 0 out of 5 stars0 ratingsA Theory of Cross-Spaces. (AM-26), Volume 26 Rating: 0 out of 5 stars0 ratingsProbleme General de la Stabilite du Mouvement. (AM-17), Volume 17 Rating: 0 out of 5 stars0 ratingsThe Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5 Rating: 0 out of 5 stars0 ratingsLectures on Differential Equations. (AM-14), Volume 14 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-20), Volume I Rating: 0 out of 5 stars0 ratingsConvergence and Uniformity in Topology. (AM-2), Volume 2 Rating: 0 out of 5 stars0 ratingsAn Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4 Rating: 0 out of 5 stars0 ratingsAn Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18 Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-21), Volume 1: Measures and Integrals. (AM-21) Rating: 0 out of 5 stars0 ratingsOrder-Preserving Maps and Integration Processes. (AM-31), Volume 31 Rating: 0 out of 5 stars0 ratingsSurface Area. (AM-35), Volume 35 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Partial Differential Equations. (AM-33), Volume 33 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-24), Volume I Rating: 0 out of 5 stars0 ratingsTopological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15 Rating: 0 out of 5 stars0 ratingsLectures on Fourier Integrals. (AM-42), Volume 42 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Riemann Surfaces. (AM-30), Volume 30 Rating: 0 out of 5 stars0 ratings
Related ebooks
Outer Billiards on Kites (AM-171) Rating: 0 out of 5 stars0 ratingsA Rational Finite Element Basis Rating: 0 out of 5 stars0 ratingsMultiparameter eigenvalue problems Rating: 0 out of 5 stars0 ratingsAlgebraic Curves over a Finite Field Rating: 5 out of 5 stars5/5Spherical CR Geometry and Dehn Surgery (AM-165) Rating: 0 out of 5 stars0 ratingsAn Invitation to Modern Number Theory Rating: 0 out of 5 stars0 ratingsIntroductory Calculus: With Analytic Geometry and Linear Algebra Rating: 4 out of 5 stars4/5Oriented Projective Geometry: A Framework for Geometric Computations Rating: 0 out of 5 stars0 ratingsAutomated Structural Analysis: An Introduction Rating: 0 out of 5 stars0 ratingsTime Series: Applications to Finance Rating: 4 out of 5 stars4/5Optimal Transport Methods in Economics Rating: 5 out of 5 stars5/5Mathematical Methods: A Course of Mathematics for Engineers and Scientists Rating: 0 out of 5 stars0 ratingsQuaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality Rating: 0 out of 5 stars0 ratingsMathematical Methods for Mathematicians, Physical Scientists and Engineers Rating: 0 out of 5 stars0 ratingsIntroduction to Combinatorics Rating: 5 out of 5 stars5/5Engineering Dynamics: A Comprehensive Introduction Rating: 4 out of 5 stars4/5Building and Solving Mathematical Programming Models in Engineering and Science Rating: 4 out of 5 stars4/5Prime-Detecting Sieves (LMS-33) Rating: 0 out of 5 stars0 ratingsReflective Optics Rating: 0 out of 5 stars0 ratingsCalculus: Introductory Theory and Applications in Physical and Life Science Rating: 1 out of 5 stars1/5Sixth Form Pure Mathematics: Volume 1 Rating: 3 out of 5 stars3/5Arithmetic Applied Mathematics Rating: 4 out of 5 stars4/5Manifold Theory: An Introduction for Mathematical Physicists Rating: 0 out of 5 stars0 ratingsHonors Calculus Rating: 0 out of 5 stars0 ratingsApplied Iterative Methods Rating: 0 out of 5 stars0 ratingsCombinatorial Optimization Rating: 5 out of 5 stars5/5Forecasting Economic Time Series Rating: 5 out of 5 stars5/5Orbital Mechanics: For Engineering Students Rating: 5 out of 5 stars5/5Lambda-Matrices and Vibrating Systems Rating: 3 out of 5 stars3/5
Mathematics For You
My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5Calculus Made Easy Rating: 4 out of 5 stars4/5Algebra - The Very Basics Rating: 5 out of 5 stars5/5Standard Deviations: Flawed Assumptions, Tortured Data, and Other Ways to Lie with Statistics Rating: 4 out of 5 stars4/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsReal Estate by the Numbers: A Complete Reference Guide to Deal Analysis Rating: 0 out of 5 stars0 ratingsThe Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game - Updated Edition Rating: 4 out of 5 stars4/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5The Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5Flatland Rating: 4 out of 5 stars4/5Algebra I For Dummies Rating: 4 out of 5 stars4/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Logicomix: An epic search for truth Rating: 4 out of 5 stars4/5The Math of Life and Death: 7 Mathematical Principles That Shape Our Lives Rating: 4 out of 5 stars4/5Is God a Mathematician? Rating: 4 out of 5 stars4/5Basic Math Notes Rating: 5 out of 5 stars5/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5The Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5Relativity: The special and the general theory Rating: 5 out of 5 stars5/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5
Reviews for The Plaid Model
0 ratings0 reviews