圖書信息
書名：Symmetries(對稱)
ISBN：9787302214786
作者：Johnson, D.L.著
定價：34元
出版日期：2009-11-1
出版社：清華大學出版社
圖書簡介
本書研究空間幾何中的各種對稱，介紹相關的對稱群；以通俗易懂的方式講述幾何與群的本質，以及兩者之間的聯繫（即對稱）。書中有大量習題並附部分習題答案或提示。本書是一本優秀的數學教材，適用於數學系本科生和其他專業對數學有興趣的本科生用作數學參考書或課外讀物。
目錄
Contents
1. Metric Spaces and their Groups
1.1 MetricSpaces
1.2 Isometries
1.3 Isometries of the Real Line
1.4 Matters Arising
1.5 Symmetry Groups
2. IsometriesofthePlane
2.1 Congruent Triangles
2.2 IsometriesofDifferentTypes
2.3 The Normal Form Theorem
2.4 Conjugationoflsometries
3. Some Basic Group Theory
3.1 Groups
3.2 Subgroups
3.3 Factor Groups
3.4 Semidirect Products
4. Products of Reflections
4.1 The Product of Two Reflections
4.2 Three Reflections
4.3 Four or More
5. Generators and Relations
5.1 Examples
5.2 Semidirect Products Again
5.3 Change of Presentation
5.4 Triangle Groups
5.5 Abelian Groups
6. Discrete Subgroups of the Euclidean Group
6.1Leonardo's Theorem
6.2 ATrichotomy
6.3Friezes and Their Groups
6.4The Classification
7 Plane Crystallographic Groups' OP Case
7.1 The Crystallographic Restriction
7.2 TheParametern
7.3 The Choice of b
7.4 Conclusion
8. Plane Crystallographic Groups: OR Case
8.1A Useful Dichotomy
8.2 The Case n—1
8.3 The Case n—2
8.4 The Case n—3
8.5 The Case n—4
8.6 The Case n—5
9. Tessellations of the Plane
9.1 Regular Tessellations
9.2 Descendants of (4, 4)
9.3 Bricks
9.4 Split Bricks
9.5 Descendants of (3, 6)
10. Tessellations of the Sphere
0.1 Spherical Geometry
10.2 The Spherical Excess
10.3 Tessellations of- the--Sphere
10.4 The-Platonic Solids
10.5 Symmetry Groups
11. Triangle Groups
11.1 The Euclidean Case
11.2 The Elliptic Case
11.3 The Hyperbolic Case
11.4 Coxeter Groups
12. Regular Polytopes
12.1 The Standard Examples
12.2 The Exceptional Types in Dimension Four.
12.3 Three Concepts and a Theorem
12.4 Schliifli's Theorem
Solutions
Guide to the Literature
Index of Notation
Index
