Symmetry

Name: Symmetry
ISBN: 9787301291719

外尔Aug 2025

4.5

Word count: 103K words
Chapters: 16
ISBN: 9787301291719

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Summary

Symmetry is an important concept in mathematics with a very early origin. It is quite common in human production and life; for example, symmetry can be seen in architecture, clothing, decorative patterns and many other fields. This book is a mathematical summary and discussion of symmetry, covering bilateral symmetry, translational symmetry, rotational symmetry and related symmetries, decorative symmetry, and more. The importance of symmetry to modern physics and to modern science as a whole is well known. Weyl, a great mathematician and one of the pioneers of applying symmetry in modern physics, discusses this topic—abstract and difficult for ordinary people—in an accessible yet rigorous style, so that general readers can appreciate the intrinsic charm and profundity of modern mathematics. Yang Chen-Ning commented that this book is a beautiful book!

Editor's review

Weyl writes about symmetry as a mathematician, yet general readers can follow. The book moves from bilateral, translational and rotational symmetry to decorative symmetry, gathering phenomena common in architecture, clothing and patterns into a mathematical summary and discussion, then extending to the importance of symmetry in modern physics and modern science as a whole. The author is one of the pioneers of applying symmetry in modern physics, so the discussion has both origins and destinations. The highlight is accessibility with rigor: concepts are not avoided, but presented in an accessible style, letting readers appreciate the intrinsic charm and profundity of modern mathematics. Yang Chen-Ning called it “a beautiful book,” a reliable entry point to the subject. Suitable for slow reading by those interested in the intersection of mathematics and physics, and as a supplement to general reading.

Who it's for

A good fit for

Readers interested in mathematical concepts with some science background
Physics enthusiasts wanting to understand symmetry's role in modern physics
General readers who enjoy thoughtful non-fiction and slow reading
Mathematics or physics students as extracurricular reading

Not a good fit for

Readers with no mathematical background seeking zero-threshold reading
Readers expecting lots of illustrations and quick browsing
Students looking for exercise books or exam-prep materials

Reading tips

Start with decorative symmetry and use everyday examples to build intuition
Slow down at mathematical discussions and sketch diagrams to aid understanding
After finishing, revisit the sections on symmetry and physics to connect the overall thread
Compare with symmetry in architecture and art to deepen understanding

版权信息
导读Introduction to Chinese Version
序言及文献评注Preface and Bibliographical Remarks
弁言Preface to the Series of the Great Classics in Science
一、双侧对称性Part Ⅰ Bilateral Symmetry
二、平移对称性、旋转对称性和有关的对称性Part Ⅱ Translatory,Rotationaland Related
三、装饰对称性Part Ⅲ Ornamental Symmetry
四、晶体·对称性的一般数学概念Part Ⅳ Crystal· The General Mathematical Idea
致谢Acknowledgements
注释Notes
附录ⅠAppendix Ⅰ
A 确定三维空间中由真旋转构成的所有有限群
B 计入非真旋转
附录ⅡAppendix Ⅱ
A 拓扑和抽象代数：理解数学的两种途径
B 心蕴诗魂的数学家与父亲

FAQ

Can I understand it without advanced mathematics?

The discussion is accessible but rigorous. Readers with middle-school mathematics who are willing to read slowly can follow most of it; abstract mathematical passages may require rereading or supplementary background knowledge.

Is the book mainly about mathematics or physics?

The main body is a mathematical summary and discussion of symmetry, including bilateral, translational, rotational and decorative symmetry, while also discussing symmetry's importance to modern physics and modern science as a whole—an interdisciplinary topic of mathematics and physics.

What does Yang Chen-Ning's comment mean?

The material records Yang Chen-Ning's comment that this book is a beautiful book, reflecting a physicist's recognition of its quality and serving as a reference for readability; actual reading experience varies by person.

Is it suitable as general reading?

Yes. The book discusses an abstract and difficult topic in an accessible style, enabling general readers to appreciate the intrinsic charm of modern mathematics; it can serve as general reading in mathematics and science.

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About the author

外尔 Author

Weyl is an author with works spanning the intersections of mathematics, physics, and philosophy. Publicly available biographical information about him is limited, and his birth and death years, nationality, and educational background are not specified in the existing materials. Three of his works are included here: The Philosophy of Mathematics and Natural Science, Symmetry, and The Principles of Relativity, showing that his writing crosses the categories of Western philosophy and popular science. He tends to begin with specific concepts and principles, discussing mathematical structures, physical theories, and philosophical reflection within a single framework; his style is rigorous and focused on tracing intellectual lines of thought. Symmetry uses symmetry as a thread linking geometry, art, and natural phenomena, The Principles of Relativity concentrates on the foundations and derivations of the theory itself, and The Philosophy of Mathematics and Natural Science further examines the philosophical premises of scientific knowledge. These works suit readers interested in the history of scientific thought and the philosophy of science, and are often regarded as reference reading for understanding the evolution of mathematical and physical ideas.