几何学史

English | PDF | 2012 | 443 Pages | ISBN : 3642291627 | 19.14 MB

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

在这本教科书中，作者以几何学最初发现的顺序大致介绍了第一年的几何。前五章展示了古希腊如何建立几何以及它在日常生活中的众多应用，并且讨论了一些关于欧几里得几何的现代研究成果。接下来的三章解释了由于笛卡尔、欧拉和高斯等人在代数领域取得的进步所导致的几何学革命。空间几何、向量代数和矩阵在第九章和第十章中进行讲解。最后一章介绍了19世纪出现的投影几何。本书配有大量例子、习题、图形和图片，既提供了动机又富有见解性的解释，并且为学生和教师 alike 提供了令人兴奋和愉快的阅读体验。

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