Geometry:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://scans.hebis.de/HEBCGI/show.pl?27868989_toc.html http://scans.hebis.de/HEBCGI/show.pl?27868989_kub.html http://scans.hebis.de/HEBCGI/show.pl?27868989_aub.html http://scans.hebis.de/HEBCGI/show.pl?27868989_rez.html http://scans.hebis.de/HEBCGI/show.pl?27868989_bio.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975311&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 587 S. graph. Darst. |
| ISBN: | 9781107647831 1107647835 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819267577301434368 |
|---|---|
| adam_text | Titel: Geometry
Autor: Brannan, David A
Jahr: 2012
Contents
Preface page xi
0 Introduction: Geometry and Geometries 1
1 Conics 5
1.1 Conic Sections and Conics 6
1.2 Properties of Conics 23
1.3 Recognizing Conics 36
1.4 Quadric Surfaces 42
1.5 Exercises 52
Summary of Chapter 1 55
2 Affine Geometry 61
2.1 Geometry and Transformations 62
2.2 Affine Transformations and Parallel Projections 70
2.3 Properties of Affine Transformations 84
2.4 Using the Fundamental Theorem of Affine Geometry 93
2.5 Affine Transformations and Conics 108
2.6 Exercises 117
Summary of Chapter 2 121
3 Projective Geometry: Lines 127
3.1 Perspective 128
3.2 The Projective Plane ]RP2 137
3.3 Projective Transformations 151
3.4 Using the Fundamental Theorem of Projective Geometry 172
3.5 Cross-Ratio 179
3.6 Exercises 192
Summary of Chapter 3 195
4 Projective Geometry: Conics 201
4.1 Projective Conics 202
4.2 Tangents 216
4.3 Theorems 229
vn
viii Contents
4.4 Applying Linear Algebra to Projective Conics 248
4.5 Duality and Projective Conics 250
4.6 Exercises 252
Summary of Chapter 4 255
5 Inversive Geometry 261
5.1 Inversion 262
5.2 Extending the Plane 276
5.3 Inversive Geometry 295
5.4 Fundamental Theorem of Inversive Geometry 310
5.5 Coaxal Families of Circles 317
5.6 Exercises 331
Summary of Chapter 5 335
6 Hyperbolic Geometry: the Poincare Model 343
6.1 Hyperbolic Geometry: the Disc Model 345
6.2 Hyperbolic Transformations 356
6.3 Distance in Hyperbolic Geometry 367
6.4 Geometrical Theorems 383
6.5 Area 401
6.6 Hyperbolic Geometry: the Half-Plane Model 412
6.7 Exercises 413
Summary of Chapter 6 417
7 Elliptic Geometry: the Spherical Model 424
7.1 Spherical Space 425
7.2 Spherical Transformations 429
7.3 Spherical Trigonometry 438
7.4 Spherical Geometry and the Extended Complex Plane 450
7.5 Planar Maps 460
7.6 Exercises 464
Summary of Chapter 7 465
8 The Kleinian View of Geometry 470
8.1 Affine Geometry 470
8.2 Projective Reflections 475
8.3 Hyperbolic Geometry and Projective Geometry 477
8.4 Elliptic Geometry: the Spherical Model 482
8.5 Euclidean Geometry 484
Summary of Chapter 8 486
Special Symbols 488
Further Reading 490
Appendix 1: A Primer of Group Theory 492
Contents
Appendix 2: A Primer of Vectors and Vector Spaces 495
Appendix 3: Solutions to the Problems 503
Chapter 1 503
Chapter 2 517
Chapter 3 526
Chapter 4 539
Chapter 5 549
Chapter 6 563
Chapter 7 574
Index 583
|
| any_adam_object | 1 |
| author | Brannan, David A. Esplen, Matthew F. Gray, Jeremy J. 1947- |
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| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
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| title | Geometry |
| title_auth | Geometry |
| title_exact_search | Geometry |
| title_full | Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray |
| title_fullStr | Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray |
| title_full_unstemmed | Geometry David A. Brannan ; Matthew F. Esplen ; Jeremy J. Gray |
| title_short | Geometry |
| title_sort | geometry |
| topic | Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometrie Lehrbuch |
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