Springer Undergraduate Mathematics Series: Symmetries (Softcover)
Springer Undergraduate Mathematics Series: Symmetries (Softcover)
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From the back cover: "Key features include:- An overview of the preliminaries from group theory and geometry
- Coverage of the discrete subgroups of the Euclidean group
- A clear and complete derivation and classification of the 17 plane crystallographic groups
- Tessellations of various spaces (they are constructed, described and classified)
- A brief introduction to hyperbolic geometry.
"Each chapter contains a number of exercises, most with solutions, and suggestions for background, alternative and further reading. The author's accessible and down-to-earth approach makes this an ideal introduction for readers in the second or third year of a mathematics undergraduate course. It is also recommended for mechanical engineers, architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry."
BRIEF CONTENTS
- 1. Metric Spaces and Their Groups
- 2. Isometries of the Plane
- 3. Some Basic Group Theory
- 4. Products of Reflection
- 5. Generators and Relations
- 6. Discrete Subgroups of the Euclidean Group
- 7. Plane Crystallographic Groups: OP Case
- 8. Plan Crystallographic Groups: OR Case
- 9. Tessellations of the Plane
- 10. Tessellations of the Sphere
- 11. Triangle Groups
- 12. Regular Polytopes
- Solutions
- Guide to the Literature
- Bibliography
- Index of Notations
- Index
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PUBLISHER: Springer-Verlag
ISBN-13: 9781852332709
ISBN-10: 1852332700