几何
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作者（美）哈茨霍恩 著
出版社世界图书出版公司
ISBN9787510033087
出版时间2011-04
装帧平装
开本24开
纸张胶版纸
定价59元
货号22473055
上书时间2024-06-30
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【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
【内容简介】:
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shou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*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。
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