幾何
出版時間：2011-4 出版社：世界圖書出版公司 作者：哈茨霍恩 頁數(shù)：526
Tag標簽：無
內容概要
本書是一部本科生水平的幾何教程。通過《幾何》可以了解作者的思想以及作者在該領域做出的重大貢獻。書中首先講述歐幾里得基礎知識，然后進一步引導讀者了解歐幾里得幾何的關鍵性內容、近期發(fā)展和更多的最新結果，許多證明可以加深對內容的理解。內容有坐標的引入、區(qū)域理論、幾何學結構和有限場擴展、平行公設歷史、多種非歐幾里得幾何和規(guī)則半規(guī)則多面體?！稁缀斡⑽?影印版)》是數(shù)學專業(yè)中等及以上水平讀者很難得的一本入門書籍。
書籍目錄
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
圖書封面
圖書標簽Tags
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評論、評分、閱讀與下載
用戶評論 (總計3條)
- 大牛寫的很基礎的書，很適合高中生讀一讀
- Robin Hartshorne is a Mathesmatician.So it is all I can say.
- 本書寫的是歐幾里德初等幾何，例如從尺規(guī)作圖方面講授它的原理，當然還包括些歷史。淺顯易懂，且世圖比較少這種書，所以算比較稀罕的。
另一方面，請奧賽者不要期待用這本書啦。里面講幾本原理，你們那些亂如麻的幾何題它是沒有的。