几何

出版时间：2011-4  出版社：世界图书出版公司  作者：哈茨霍恩  页数：526  
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内容概要

　　本书是一部本科生水平的几何教程。通过《几何》可以了解作者的思想以及作者在该领域做出的重大贡献。书中首先讲述欧几里得基础知识，然后进一步引导读者了解欧几里得几何的关键性内容、近期发展和更多的最新结果，许多证明可以加深对内容的理解。内容有坐标的引入、区域理论、几何学结构和有限场扩展、平行公设历史、多种非欧几里得几何和规则半规则多面体。《几何英文(影印版)》是数学专业中等及以上水平读者很难得的一本入门书籍。

书籍目录

chapter 1. euclid's geometry
　1. a first look at euclid's elements
　2. ruler and compass constructions
　3. euclid's axiomatic method
　4. construction of the regular pentagon
　5. some newer results
chapter 2. hilbert's axioms
　6. axioms of incidence
　7. axioms of betweenness
　8. axioms of congruence for line segments
　9. axioms of congruence for angles
　10. hilbert planes
　11. intersection of lines and circles
　12. euclidean planes
chapter 3. geometry over fields
　13. the real cartesian plane
　14. abstract fields and incidence
　15. ordered fields and betweenness
　16. congruence of segments and angles
　17. rigid motions and sas
　18. non-archimedean geometry
chapter 4. segment arithmetic
　19. addition and multiplication of line segments
　20. similar triangles
　21. introduction of coordinates
chapter 5. area
　22. area in euclid's geometry
　23. measure of area functions
　24. dissection
　25. quadrature circuli
　26. euclid's theory of volume
　27. hilbert's third problem
chapter 6. construction problems and field extensions
　28. three famous problems
　29. the regular 17-sided polygon
　30. constructions with compass and marked ruler
　31. cubic and quartic equations
　32. appendix: finite field extensions
chapter 7. non-euclidean geometry
　33. history of the parallel postulate
　34. neutral geometry
　35. archimedean neutral geometry
　36. non-euclidean area
　37. circular inversion
　38. digression: circles determined by three conditions
　39. the poincare model
　40. hyperbolic geometry
　41. hilbert's arithmetic of ends
　42. hyperbolic trigonometry
　43. characterization of hilbert planes
chapter 8. polyhedra
　44. the five regular solids
　45. euler's and cauchy's theorems
　46. semiregular and face-regular polyhedra
　47. symmetry groups of polyhedra
appendix: brief euclid
notes
references
list of axioms
index of euclid's propositions
index

用户评论 (总计3条)

•   大牛写的很基础的书，很适合高中生读一读
•   Robin Hartshorne is a Mathesmatician.So it is all I can say.
•   本书写的是欧几里德初等几何，例如从尺规作图方面讲授它的原理，当然还包括些历史。浅显易懂，且世图比较少这种书，所以算比较稀罕的。
  另一方面，请奥赛者不要期待用这本书啦。里面讲几本原理，你们那些乱如麻的几何题它是没有的。