Affine and projective geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY u.a.
Wiley
1995
|
| Schriftenreihe: | A Wiley interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 229 S. graph. Darst. |
| ISBN: | 0471113158 |
Internformat
MARC
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| 245 | 1 | 0 | |a Affine and projective geometry |c M. K. Bennett |
| 264 | 1 | |a New York, NY u.a. |b Wiley |c 1995 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
List of Examples xi
Special Symbols xiii
Preface xv
1. Introduction 1
1.1. Methods of Proof, 1
1.2. Some Greek Geometers, 2
1.3. Cartesian Geometry, 6
1.4. Hilbert s Axioms, 11
1.5. Finite Coordinate Planes, 12
1.6. The Theorems of Pappus and Desargues, 14
Suggested Reading, 17
2. Affine Planes 18
2.1. Definitions and Examples, 18
2.2. Some Combinatorial Results, 23
2.3. Finite Planes, 28
2.4. Orthogonal Latin Squares, 33
2.5. Affine Planes and Latin Squares, 36
2.6. Projective Planes, 41
Suggested Reading, 46
3. Desarguesian Affine Planes 47
3.1. The Fundamental Theorem, 47
3.2. Addition on Lines, 48
3.3. Desargues Theorem, 50
3.4. Properties of Addition in Affine Planes, 55
3.5. The Converse of Desargues Theorem, 58
vii
viii Contents
3.6. Multiplication on Lines of an Affine Plane, 62
3.7. Pappus Theorem and Further Properties, 66
Suggested Reading, 70
4. Introducing Coordinates 71
4.1. Division Rings, 71
4.2. Isomorphism, 74
4.3. Coordinate Affine Planes, 76
4.4. Coordinatizing Points, 82
4.5. Linear Equations, 86
4.6 The Theorem of Pappus, 90
Suggested Reading, 92
5. Coordinate Projective Planes 93
5.1. Projective Points and Homogeneous Equations in
D3, 93
5.2. Coordinate Projective Planes, 96
5.3. Coordinatization of Desarguesian Projective Planes, 99
5.4. Projective Conies, 102
5.5. Pascal s Theorem, 106
5.6. Non-Desarguesian Coordinate Planes, 110
5.7. Some Examples of Veblen-Wedderburn Systems, 114
5.8. A Projective Plane of Order 9, 117
Suggested Reading, 122
6. Affine Space 123
6.1. Synthetic Affine Space, 123
6.2. Flats in Affine Space, 128
6.3. Desargues Theorem, 131
6.4. Coordinatization of Affine Space, 134
Suggested Reading, 143
7. Projective Space 144
7.1 Synthetic Projective Space, 144
7.2. Planes in Projective Space, 147
7.3. Dimension, 150
7.4. Consequences of Desargues Theorem, 154
7.5. Coordinates in Projective Space, 159
Suggested Reading, 164
8. Lattices of Flats 165
8.1. Closure Spaces, 165
8.2. Some Properties of Closure Spaces, 167
Contents ix
8.3. Projective Closure Spaces, 170
8.4. Introduction to Lattices, 171
8.5. Bounded Lattices; Duality, 174
8.6. Distributive, Modular, and Atomic Lattices, 177
8.7. Complete Lattices and Closure Spaces, 181
Suggested Reading, 185
9. Collineations 186
9.1. General Collineations, 186
9.2. Automorphisms of Planes, 190
9.3. Perspectivities of Projective Spaces, 195
9.4. The Fundamental Theorem of Projective Geometry,
199
9.5. Projectivities and Linear Transformations, 205
9.6. Collineations and Commutativity, 209
Suggested Reading, 211
Appendix A. Algebraic Background 212
A.l. Fields, 212
A.2. The Integers Mod n, 214
A.3. Finite Fields, 217
Suggested Reading, 220
Appendix B. Hilbert s Example of a Noncommutative
Division Ring 221
Suggested Reading, 223
Index 225
|
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| id | DE-604.BV010477265 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:53:09Z |
| institution | BVB |
| isbn | 0471113158 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006981022 |
| oclc_num | 247026503 |
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| owner | DE-91 DE-BY-TUM DE-20 DE-703 DE-11 DE-29T |
| owner_facet | DE-91 DE-BY-TUM DE-20 DE-703 DE-11 DE-29T |
| physical | XVI, 229 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley interscience publication |
| spelling | Bennett, Mary K. Verfasser aut Affine and projective geometry M. K. Bennett New York, NY u.a. Wiley 1995 XVI, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley interscience publication Affine Geometrie (DE-588)4141566-8 gnd rswk-swf Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Affine Geometrie (DE-588)4141566-8 s DE-604 Projektive Geometrie (DE-588)4047436-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006981022&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bennett, Mary K. Affine and projective geometry Affine Geometrie (DE-588)4141566-8 gnd Projektive Geometrie (DE-588)4047436-7 gnd |
| subject_GND | (DE-588)4141566-8 (DE-588)4047436-7 |
| title | Affine and projective geometry |
| title_auth | Affine and projective geometry |
| title_exact_search | Affine and projective geometry |
| title_full | Affine and projective geometry M. K. Bennett |
| title_fullStr | Affine and projective geometry M. K. Bennett |
| title_full_unstemmed | Affine and projective geometry M. K. Bennett |
| title_short | Affine and projective geometry |
| title_sort | affine and projective geometry |
| topic | Affine Geometrie (DE-588)4141566-8 gnd Projektive Geometrie (DE-588)4047436-7 gnd |
| topic_facet | Affine Geometrie Projektive Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006981022&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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