Miles of Tiles
About this Title
Charles Radin, University of Texas, Austin, Austin, TX
Publication: The Student Mathematical Library
Publication Year 1999: Volume 1
ISBNs: 978-0-8218-1933-3 (print); 978-1-4704-2122-9 (online)
MathSciNet review: MR1707270
MSC: Primary 52C22; Secondary 20H15, 37A99, 37B50, 52C23, 82D25
“In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics—mathematics unforeseen from the motivating problem …”
—from the Preface
The common thread throughout this book is aperiodic tilings; the best-known example is the “kite and dart” tiling. This tiling has been widely discussed, particularly since 1984 when it was adopted to model quasicrystals. The presentation uses many different areas of mathematics and physics to analyze the new features of such tilings. Although many people are aware of the existence of aperiodic tilings, and maybe even their origin in a question in logic, not everyone is familiar with their subtleties and the underlying rich mathematical theory. For the interested reader, this book fills that gap.
Understanding this new type of tiling requires an unusual variety of specialties, including ergodic theory, functional analysis, group theory and ring theory from mathematics, and statistical mechanics and wave diffraction from physics. This interdisciplinary approach also leads to new mathematics seemingly unrelated to the tilings. Included are many worked examples and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience.
Advanced undergraduates, graduate students, and research mathematicians.
Table of Contents
- Chapter 1. Ergodic theory
- Chapter 2. Physics (for mathematicians)
- Chapter 3. Order
- Chapter 4. Symmetry
- Chapter 5. Conclusion
- Appendix I. Geometry
- Appendix II. Algebra
- Appendix III. Analysis