Rating: 1 out of 5 stars
1/5
Ebook193 pages5 hours
The Plaid Model: (AMS-198)
Rating: 0 out of 5 stars
()
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.
Author
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)
Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104 Functional Operators, Volume 1: Measures and Integrals. (AM-21) Rating: 0 out of 5 stars0 ratingsDiscrete Series of GLn Over a Finite Field. (AM-81), Volume 81 Rating: 0 out of 5 stars0 ratingsClassifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 Rating: 0 out of 5 stars0 ratingsC*-Algebra Extensions and K-Homology. (AM-95), Volume 95 Rating: 0 out of 5 stars0 ratingsTopics in Transcendental Algebraic Geometry. (AM-106), Volume 106 Rating: 0 out of 5 stars0 ratingsHarmonic Analysis in Phase Space. (AM-122), Volume 122 Rating: 0 out of 5 stars0 ratingsAutomorphic Forms on Adele Groups. (AM-83), Volume 83 Rating: 0 out of 5 stars0 ratingsLinear Inequalities and Related Systems Rating: 0 out of 5 stars0 ratingsCharacteristic Classes. (AM-76), Volume 76 Rating: 5 out of 5 stars5/5Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 Rating: 5 out of 5 stars5/5Infinite Loop Spaces (AM-90), Volume 90: Hermann Weyl Lectures, The Institute for Advanced Study. (AM-90) Rating: 0 out of 5 stars0 ratingsScattering Theory for Automorphic Functions. (AM-87), Volume 87 Rating: 0 out of 5 stars0 ratingsStrong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 Rating: 0 out of 5 stars0 ratingsAdvances in Game Theory Rating: 0 out of 5 stars0 ratingsInvariant Forms on Grassmann Manifolds. (AM-89), Volume 89 Rating: 0 out of 5 stars0 ratingsK-Theory of Forms. (AM-98), Volume 98 Rating: 0 out of 5 stars0 ratingsRiemann Surfaces and Related Topics (AM-97), Volume 97: Proceedings of the 1978 Stony Brook Conference. (AM-97) Rating: 0 out of 5 stars0 ratingsCharacters of Reductive Groups over a Finite Field. (AM-107), Volume 107 Rating: 0 out of 5 stars0 ratingsAdvances in the Theory of Riemann Surfaces. (AM-66), Volume 66 Rating: 0 out of 5 stars0 ratingsSeminar on Micro-Local Analysis. (AM-93), Volume 93 Rating: 0 out of 5 stars0 ratingsRecent Developments in Several Complex Variables. (AM-100), Volume 100 Rating: 0 out of 5 stars0 ratingsCombinatorial Group Theory and Topology. (AM-111), Volume 111 Rating: 0 out of 5 stars0 ratingsEntire Holomorphic Mappings in One and Several Complex Variables. (AM-85), Volume 85 Rating: 0 out of 5 stars0 ratingsHyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136 Rating: 0 out of 5 stars0 ratingsThree-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 Rating: 0 out of 5 stars0 ratingsAlgebraic Topology and Algebraic K-Theory (AM-113), Volume 113: Proceedings of a Symposium in Honor of John C. Moore. (AM-113) Rating: 0 out of 5 stars0 ratingsFoundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 Rating: 0 out of 5 stars0 ratingsRandom Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 Rating: 0 out of 5 stars0 ratings
Related ebooks
Outer Billiards on Kites Rating: 0 out of 5 stars0 ratingsAlgebraic Curves over a Finite Field Rating: 5 out of 5 stars5/5Spherical CR Geometry and Dehn Surgery Rating: 0 out of 5 stars0 ratingsAn Invitation to Modern Number Theory 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 stars5/5Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality Rating: 0 out of 5 stars0 ratingsEngineering 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 ratingsHonors Calculus Rating: 0 out of 5 stars0 ratingsCombinatorial Optimization Rating: 5 out of 5 stars5/5Control Theoretic Splines: Optimal Control, Statistics, and Path Planning Rating: 5 out of 5 stars5/5An Introduction to Metric Spaces and Fixed Point Theory Rating: 0 out of 5 stars0 ratingsTheoretical Global Seismology Rating: 4 out of 5 stars4/5Schaum's Outline of Optics Rating: 0 out of 5 stars0 ratingsFundamentals of Ocean Climate Models Rating: 0 out of 5 stars0 ratingsModern Astrodynamics: Fundamentals and Perturbation Methods Rating: 0 out of 5 stars0 ratingsThe Standard Model in a Nutshell Rating: 0 out of 5 stars0 ratingsComputational Chemistry: A Practical Guide for Applying Techniques to Real World Problems Rating: 4 out of 5 stars4/5Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics Rating: 0 out of 5 stars0 ratingsThe Calculus Lifesaver: All the Tools You Need to Excel at Calculus Rating: 4 out of 5 stars4/5Wave Scattering by Time-Dependent Perturbations: An Introduction Rating: 5 out of 5 stars5/5Analysis in Vector Spaces Rating: 0 out of 5 stars0 ratingsAntennas: From Theory to Practice Rating: 0 out of 5 stars0 ratingsFundamentals of Matrix Computations Rating: 0 out of 5 stars0 ratingsLearning and Expectations in Macroeconomics Rating: 4 out of 5 stars4/5Optical Metrology Rating: 0 out of 5 stars0 ratingsIntroductory Lectures on Equivariant Cohomology Rating: 0 out of 5 stars0 ratings
Mathematics For You
What If?: Serious Scientific Answers to Absurd Hypothetical Questions Rating: 5 out of 5 stars5/5Algorithms to Live By: The Computer Science of Human Decisions Rating: 4 out of 5 stars4/5The Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5Build a Mathematical Mind - Even If You Think You Can't Have One Rating: 0 out of 5 stars0 ratingsThe Art of Logic: How to Make Sense in a World that Doesn't Rating: 0 out of 5 stars0 ratingsSummary of The Black Swan: by Nassim Nicholas Taleb | Includes Analysis Rating: 5 out of 5 stars5/5Algebra - The Very Basics Rating: 5 out of 5 stars5/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5My Best Mathematical and Logic Puzzles Rating: 4 out of 5 stars4/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5Geometry For Dummies Rating: 4 out of 5 stars4/5Calculus For Dummies Rating: 4 out of 5 stars4/5How to Solve It: A New Aspect of Mathematical Method Rating: 4 out of 5 stars4/5Statistics: a QuickStudy Laminated Reference Guide Rating: 0 out of 5 stars0 ratingsHow Minds Change: The New Science of Belief, Opinion and Persuasion Rating: 0 out of 5 stars0 ratingsThe Art of Statistical Thinking Rating: 5 out of 5 stars5/5Calculus Essentials For Dummies Rating: 5 out of 5 stars5/5Logicomix: An epic search for truth Rating: 4 out of 5 stars4/5Mental Math: Tricks To Become A Human Calculator Rating: 5 out of 5 stars5/5Think Like A Maths Genius: The Art of Calculating in Your Head Rating: 0 out of 5 stars0 ratingsMental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5Mathematics for the Nonmathematician Rating: 4 out of 5 stars4/5Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models Rating: 5 out of 5 stars5/5Learn Game Theory: Strategic Thinking Skills, #1 Rating: 5 out of 5 stars5/5The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry Rating: 3 out of 5 stars3/5
Related articles
Dynamic Drive Part Two Racecar EngineeringArticle
Dynamic Drive Part Two
Dec 2, 2022
6 min readWilliam Optics RedCat 61 WIFD Petzval apo refractor BBC Sky at NightArticle
William Optics RedCat 61 WIFD Petzval apo refractor
Oct 19, 2023
Our experts review the latest kit • Price £1,629 • Optics Petzval design • Aperture 61mm • Focal length 300mm, f/4.9 • Tube length 365mm • Focuser Dual-speed WIFD • Extras RedCat tube rings, Vixen dovetail bar, saddle handle bar, integrated Bahtinov
3 min readEffects Sims: Body Parts And All 3D WorldArticle
Effects Sims: Body Parts And All
Apr 17, 2019
1 min readWilliam Optics Pleiades 68 astrograph BBC Sky at NightArticle
William Optics Pleiades 68 astrograph
Dec 12, 2024
4 min readThe Quest for Round Stars Australian Sky & TelescopeArticle
The Quest for Round Stars
May 29, 2019
8 min readThe Lowdown On PEI And CDI Systems Classic Motorcycle MechanicsArticle
The Lowdown On PEI And CDI Systems
Mar 15, 2021
Right then, how does a PEI system work? PEI, slightly unfortunately, stands for Pointless Electronic Ignition. Manufactured by Kokusan Denki, it is, in fact, a CDI system and I believe first appeared on the Suzuki moto-cross and larger trail bikes
2 min readIndex Of Performance Racecar EngineeringArticle
Index Of Performance
Nov 1, 2019
6 min readQHYCCD’s New 60-megapixel Camera Australian Sky & TelescopeArticle
QHYCCD’s New 60-megapixel Camera
Jun 3, 2020
THERE’S A LOT TO TALK ABOUT with the new QHY600M camera from QHYCCD, so let’s jump right in. And the first thing there’s a lot of is pixels — 62,393,796 of them, according to the spec sheet for Sony’s IMX455 back-side illuminated, full-frame, CMOS se
7 min readPen To Paper Racecar EngineeringArticle
Pen To Paper
Feb 2, 2024
Over the last couple of months, I have been working with a number of junior engineers at senior undergraduate and junior postgraduate level. While their enthusiasm has never been in question, I am shocked by the lack of basic skills I am seeing. The
7 min readMissing Links Racecar EngineeringArticle
Missing Links
Aug 5, 2022
Over the last couple of months, I have been working with a number of junior engineers at senior undergraduate level and junior post graduate level. While their enthusiasm has never been in question, I am shocked by the lack of basic skills I am seein
7 min read
Reviews for The Plaid Model
Rating: 0 out of 5 stars
0 ratings
0 ratings0 reviews
Book preview
The Plaid Model - Richard Evan Schwartz
Enjoying the preview?
Page 1 of 1