

Softcover ISBN: | 978-1-4704-7461-4 |
Product Code: | MBK/142.S |
List Price: | $59.00 |
MAA Member Price: | $53.10 |
AMS Member Price: | $47.20 |
Sale Price: | $38.35 |
eBook ISBN: | 978-1-4704-7101-9 |
Product Code: | MBK/142.E |
List Price: | $59.00 |
MAA Member Price: | $53.10 |
AMS Member Price: | $47.20 |
Sale Price: | $38.35 |
Softcover ISBN: | 978-1-4704-7461-4 |
eBook: ISBN: | 978-1-4704-7101-9 |
Product Code: | MBK/142.S.B |
List Price: | $118.00 $88.50 |
MAA Member Price: | $106.20 $79.65 |
AMS Member Price: | $94.40 $70.80 |
Sale Price: | $76.70 $57.53 |


Softcover ISBN: | 978-1-4704-7461-4 |
Product Code: | MBK/142.S |
List Price: | $59.00 |
MAA Member Price: | $53.10 |
AMS Member Price: | $47.20 |
Sale Price: | $38.35 |
eBook ISBN: | 978-1-4704-7101-9 |
Product Code: | MBK/142.E |
List Price: | $59.00 |
MAA Member Price: | $53.10 |
AMS Member Price: | $47.20 |
Sale Price: | $38.35 |
Softcover ISBN: | 978-1-4704-7461-4 |
eBook ISBN: | 978-1-4704-7101-9 |
Product Code: | MBK/142.S.B |
List Price: | $118.00 $88.50 |
MAA Member Price: | $106.20 $79.65 |
AMS Member Price: | $94.40 $70.80 |
Sale Price: | $76.70 $57.53 |
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Book Details2022; 298 ppMSC: Primary 05; 52
Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications.
Furthermore, tiling theory happens to be an area where many of the subfields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject.
This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.
Preview some of these beautiful and intricate patterns here.
ReadershipUndergraduate and graduate students and researchers interested in tilings and tessellations.
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Table of Contents
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Chapters
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Introduction
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Introdction to tiling
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Types of tilings
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Aperiodic tilings
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Tilings in other geometries and other dimensions
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Appendix
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Additional Material
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Reviews
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The merit of this book...lies not in its depth or novelty, but in its clear and accessible treatment of the subject and its imaginative arrangement. The author's creative streak shines through again and again in the many color illustrations. Those who know other books by Colin Adams know what is meant. This makes this book a valuable and fruitful read, especially for the non-mathematically educated reader. (translated)
Dirk Frettlöh, Mathematische Semesterberichte -
In his book, Adams provides many fantastic hiking paths suitable for a wide range of readers. The paths are all walkable, and there is no need to bring ropes or carabiners. The hiking paths contain many scenic points where we can take rest and see interesting tilings. Occasionally along the path, the dimension leaps from 2 to 3. A hiker might notice that the metric system changes from Euclidean to hyperbolic. The paths are open-ended with the possibility that a hiker constructs a brand new path to a new scenic point.
Keiko Kawamuro (University of Iowa), AMS Notices
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications.
Furthermore, tiling theory happens to be an area where many of the subfields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject.
This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.
Preview some of these beautiful and intricate patterns here.
Undergraduate and graduate students and researchers interested in tilings and tessellations.
-
Chapters
-
Introduction
-
Introdction to tiling
-
Types of tilings
-
Aperiodic tilings
-
Tilings in other geometries and other dimensions
-
Appendix
-
The merit of this book...lies not in its depth or novelty, but in its clear and accessible treatment of the subject and its imaginative arrangement. The author's creative streak shines through again and again in the many color illustrations. Those who know other books by Colin Adams know what is meant. This makes this book a valuable and fruitful read, especially for the non-mathematically educated reader. (translated)
Dirk Frettlöh, Mathematische Semesterberichte -
In his book, Adams provides many fantastic hiking paths suitable for a wide range of readers. The paths are all walkable, and there is no need to bring ropes or carabiners. The hiking paths contain many scenic points where we can take rest and see interesting tilings. Occasionally along the path, the dimension leaps from 2 to 3. A hiker might notice that the metric system changes from Euclidean to hyperbolic. The paths are open-ended with the possibility that a hiker constructs a brand new path to a new scenic point.
Keiko Kawamuro (University of Iowa), AMS Notices