本书是英国皇家学会院士H.S.M.考克斯特所著的几何学名著。考克斯特用现代的观点阐释了从欧几里得平面几何到仿射几何、射影几何、微分几何和拓扑等经典几何的内容。书中汇集了基础几何的各种定理、变换、几种几何的公理化发展、曲线和曲面的微分几何以及曲面的拓扑等主题。正如考克斯特在序言中所说,“贯穿整部作品的统一主线是变换,或者说是对称性的思想”。变换提供了动态的,而非静态的几何观点。本书被认为是最重要的几何学书籍之一,任何对几何感兴趣的读者都应该阅读。
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Coxeter presents classical style geometry in 22 chapters, which are reasonably self-contained, though tied together by a modern spirit of reinterpretation of classical matter.
——Hans Freudenthal (Bulletin of the American Mathematical Society)
The range of subjects is so great that anyone with any capacity for appreciating geometry is very likely to find something in this book to arrest and edify him.
——Howard Levi (The Journal of Philosophy)
I consider it to be one of the most important books on geometry to be published for many years, and would urge all those who teach the subject to get a copy.
——Eric John Fyfe Primrose (The Mathematical Gazette)