Billiards, Surfaces, and Geometry

A Problem-Centered Approach

Diana Davis (Autor)

Buch | Softcover

241 Seiten

2026
American Mathematical Society (Verlag)
978-1-4704-8379-1 (ISBN)

Noch nicht erschienen (ca. Oktober 2026)
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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.

Diana Davis, Phillips Exeter Academy, New Hampshire.

Introduction to billiards in many forms
Trajectories, automorphisms, and continued fractions
Periodicity everywhere
Cylinders and automorhpisms
Further topics and tools
A short primer on matrix actions in the plane
How to teach a problem-centered course
Image credits
Hints for selected problems
Bibliography
Glossary of key terms
Index of terms
Index of people

Erscheint lt. Verlag	1.10.2026
Reihe/Serie	Student Mathematical Library
Verlagsort	Providence
Sprache	englisch
Maße	140 x 216 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-8379-3 / 1470483793
ISBN-13	978-1-4704-8379-1 / 9781470483791
Zustand	Neuware