This richly illustrated text guides readers to discover the beautiful structure of mathematical billiards. Centered around expertly designed problem sets, the book incrementally builds up ideas through threads of related problems, fostering curiosity, exploration, and conversation. Working through the problems, the reader builds an understanding of foundational results, useful techniques, and key examples, all the way up to current research, while hands-on construction activities offer an opportunity to explore phenomena in three dimensions. Beginning with the square billiard table, the opening chapters explore periodic billiard paths in depth, including connections to continued fractions and symbolic dynamics. From this foundation, the book goes on to explore billiards in triangles and other polygons, flows on translation surfaces, interval exchange transformations, outer billiards and tiling billiards, billiards on the ellipse, and many other topics. Throughout, we meet contemporary mathematicians involved in the topics covered, showcasing the research achievements of the vibrant billiards community. Billiards, Surfaces, and Geometry offers a ground level, problem-centered entry point to this exciting field. Basic knowledge of geometry and matrix transformations is assumed, though the main prerequisite is a spirit of curiosity and exploration.
- 253 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
About this book
Information
Subtopic
Mathematics GeneralIndex
MathematicsTable of contents
- Cover
- Title page
- Copyright
- Contents
- Preface
- Acknowledgments
- They did the math
- Chapter 1. Introduction to billiards in many forms
- Chapter 2. Trajectories, automorphisms, and continued fractions
- Chapter 3. Periodicity everywhere
- Chapter 4. Cylinders and automorphisms
- Chapter 5. Further topics and tools
- Appendix A. A short primer on matrix actions in the plane
- Appendix B. How to teach a problem-centered course
- Hints for selected problems
- Image credits
- Glossary of key terms
- Bibliography
- Index of people
- Index of terms
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Yes, you can access Billiards, Surfaces, and Geometry by Diana Davis in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.