Elementary geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford u.a.
Oxford Univ. Press
1993
|
| Edition: | 1. ed. |
| Series: | Oxford science publications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 307 S. graph. Darst. |
| ISBN: | 0198534574 0198534566 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
1 Axioms for geometry 1
1.1 What is geometry? 1
1.2 The axioms of incidence 5
1.3 Measurement axioms 12
1.4 Parallelograms 18
1.5 Vectors 22
1.6 Exercises 27
2 Vector geometry 28
2.1 Affine spaces 28
2.2 Position vectors 34
2.3 Some theorems in affine geometry 37
2.4 A short introduction to projective geometry 43
2.5 Exercises 47
3 Congruence axioms 51
3.1 The length of a line segment 51
3.2 The length of a vector 54
3.3 Dropping a perpendicular 57
3.4 The dot product of two vectors 59
3.5 Exercises 61
4 Euclidean geometry 63
4.1 The dot product 63
4.2 Two classic theorems 65
4.3 Angles 69
4.4 Trigonometry 73
vii
Contents
4.5 Isometries 78
4.6 Exercises 82
5 Coordinates and equations 85
5.1 Cartesian coordinates 85
5.2 Curves and equations 89
5.3 Coordinate form of an isometry 94
5.4 Change of coordinates 100
5.5 Exercises 102
6 Plane geometry 104
6.1 Orientation in the plane 104
6.2 Oriented angles 108
6.3 Polar coordinates H2
6.4 Circles in the plane 114
6.5 The use of complex numbers 120
6.6 Straightedge and compasses 123
6.7 Exercises 129
7 Conies and other curves 133
7.1 Curves and their tangents . 133
7.2 The ellipse, hyperbola, and parabola 139
7.3 More general conies 146
7.4 Intersections of lines and conies 154
7.5 A short tour around some higher degree curves 156
7.6 Exercises I64
8 Solid geometry 168
8.1 Orientation and the vector product 168
8.2 Vector equations of lines and planes 173
8.3 Isometries I76
8.4 Quaternions 183
8.5 Exercises 188
9 Area and volume 191
9.1 Polygonal regions 191
9.2 Axioms for area 194
9.3 The method of exhaustion 1
9.4 The question of consistency 205
Contents ix
9.5 Volume 207
9.6 Area integrals and Green s theorem 213
9.7 Exercises 218
10 Quadric surfaces 223
10.1 Definition and examples 223
10.2 Reduction to canonical form 227
10.3 Proof of the diagonalization theorem 231
10.4 Intersection of a quadric with a line or plane 235
10.5 Exercises 239
11 Differential geometry of curves 242
11.1 Differentiation of vector functions 242
11.2 Planetary orbits 245
11.3 The length of a curve 248
11.4 The Serret Frenet formulae 251
11.5 The general isoperimetric inequality 257
11.6 Exercises 263
12 Differential geometry of surfaces 266
12.1 Parameterized surfaces 266
12.2 Spherical geometry 274
12.3 Holonomy 277
12.4 The Gauss Bonnet theorem 282
12.5 Exercises 287
Appendix A The trigonometric functions 291
Hints and solutions to the exercises 294
Bibliography 300
Index 303
|
| any_adam_object | 1 |
| author | Roe, John |
| author_facet | Roe, John |
| author_role | aut |
| author_sort | Roe, John |
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| ctrlnum | (OCoLC)27070246 (DE-599)BVBBV009263420 |
| dewey-full | 516.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.2 |
| dewey-search | 516.2 |
| dewey-sort | 3516.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:34:07Z |
| institution | BVB |
| isbn | 0198534574 0198534566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006164781 |
| oclc_num | 27070246 |
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| physical | IX, 307 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford science publications |
| spelling | Roe, John Verfasser aut Elementary geometry John Roe 1. ed. Oxford u.a. Oxford Univ. Press 1993 IX, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Géométrie euclidienne ram Géométrie ram Meetkunde gtt Geometry Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf Elementargeometrie (DE-588)4137488-5 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 Euklidische Geometrie (DE-588)4137555-5 s Elementargeometrie (DE-588)4137488-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006164781&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roe, John Elementary geometry Géométrie euclidienne ram Géométrie ram Meetkunde gtt Geometry Euklidische Geometrie (DE-588)4137555-5 gnd Elementargeometrie (DE-588)4137488-5 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4137555-5 (DE-588)4137488-5 (DE-588)4020236-7 |
| title | Elementary geometry |
| title_auth | Elementary geometry |
| title_exact_search | Elementary geometry |
| title_full | Elementary geometry John Roe |
| title_fullStr | Elementary geometry John Roe |
| title_full_unstemmed | Elementary geometry John Roe |
| title_short | Elementary geometry |
| title_sort | elementary geometry |
| topic | Géométrie euclidienne ram Géométrie ram Meetkunde gtt Geometry Euklidische Geometrie (DE-588)4137555-5 gnd Elementargeometrie (DE-588)4137488-5 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Géométrie euclidienne Géométrie Meetkunde Geometry Euklidische Geometrie Elementargeometrie Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006164781&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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