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几何 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （美）哈茨霍恩著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510033087
- 出版时间：2011
- 标注页数：526页
- 文件大小：95MB
- 文件页数：545页
- 主题词：几何－高等学校－教材－英文
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图书目录
Introduction7
Chapter 1．Euclid's Geometry7
1．A First Look at Euclid's Elements8
2．Ruler and Compass Constructions18
3．Euclid's Axiomatic Method27
4．Construction of the Regular Pentagon45
5．Some Newer Results51
Chapter 2．Hilbert's Axioms65
6．Axioms of Incidence66
7．Axioms of Betweenness73
8．Axioms of Congruence for Line Segments81
9．Axioms of Congruence for Angles90
10．Hilbert Planes96
11．Intersection of Lines and Circles104
12．Euclidean Planes112
Chapter 3．Geometry over Fields117
13．The Real Cartesian Plane118
14．Abstract Fields and Incidence128
15．Ordered Fields and Betweenness135
16．Congruence of Segments and Angles140
17．Rigid Motions and SAS148
18．Non-Archimedean Geometry158
Chapter 4．Segment Arithmetic165
19．Addition and Multiplication of Line Segments165
20．Similar Triangles175
21．Introduction of Coordinates186
Chapter 5．Area195
22．Area in Euclid's Geometry196
23．Measure of Area Functions205
24．Dissection212
25．Quadratura Circuli221
26．Euclid's Theory of Volume226
27．Hilbert's Third Problem231
Chapter 6．Construction Problems and Field Extensions241
28．Three Famous Problems242
29．The Regular 17-Sided Polygon250
30．Constructions with Compass and Marked Ruler259
31．Cubic and Quartic Equations270
32．Appendix:Finite Field Extensions280
Chapter 7．Non-Euclidean Geometry295
33．History of the Parallel Postulate296
34．Neutral Geometry304
35．Archimedean Neutral Geometry319
36．Non-Euclidean Area326
37．Circular Inversion334
38．Digression:Circles Determined by Three Conditions346
39．The Poincaré Model355
40．Hyperbolic Geometry373
41．Hilbert's Arithmetic of Ends388
42．Hyperbolic Trigonometry403
43．Characterization of Hilbert Planes415
Chapter 8．Polyhedra435
44．The Five Regular Solids436
45．Euler's and Cauchy's Theorems448
46．Semiregular and Face-Regular Polyhedra459
47．Symmetry Groups of Polyhedra469
Appendix:Brief Euclid481
Notes487
References495
List of Axioms503
Index of Euclid's Propositions505
Index507