Foundations of Euclidean and non-Euclidean geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, [New York], [u.a.]
Dekker
1983
|
| Schriftenreihe: | Pure and applied mathematics
73 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 329 Seiten Illustrationen |
| ISBN: | 0824717481 |
Internformat
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| 245 | 1 | 0 | |a Foundations of Euclidean and non-Euclidean geometry |c Richard L. Faber |
| 264 | 1 | |a New York, [New York], [u.a.] |b Dekker |c 1983 | |
| 300 | |a xi, 329 Seiten |b Illustrationen | ||
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| 490 | 1 | |a Pure and applied mathematics |v 73 | |
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Datensatz im Suchindex
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| adam_text |
CONTENTS
PREFACE v
ACKNOWLEDGMENTS vii
I THE BEGINNINGS 1
1. Mesopotamian Mathematics 2
2. The Egyptians 25
II GREEK GEOMETRY 45
1. Thales of Miletus 46
2. The Pythagorean School 48
3. The Athenian School 53
4. Euclid 59
5. Archimedes 65
6. Apollonius 74
7. Greek Cosmology 80
III THE AXIOMATIC METHOD 91
1. Pips and Globs 91
2. Properties of Axiom Systems 105
3. Euclid and the Foundations of Geometry 108
IV HISTORY OF THE PARALLEL POSTULATE 125
1. The Parallel Postulate 125
2. Absolute Geometry 130
3. Absolute Lengths 141
ix
x CONTENTS
4. Saccheri 143
5. Lambert 147
6. The French Geometers 151
7. Wolfgang Bolyai 154
8. Gauss 155
9. J. Bolyai 160
10. Lobachevsky 162
V FUNDAMENTALS OF LOBACHEVSKIAN GEOMETRY 167
1. Parallelism of Rays 167
2. Angle of Parallelism 169
3. Parallelism of Lines—The Angle Criterion 171
4. Bisector of a Strip 172
5. Properties of n(x) 176
6. Ideal Points 181
7. Ideal Triangles 182
8. More Properties of n (x) 185
9. Divergent Lines 186
10. Ultra Ideal Points 188
11. Sheaves of Lines—Fundamental Curves 190
12. Limiting Curves 194
13. Concentric Horocycles 199
VI THE TRIGONOMETRIC FORMULAS 205
1. Perpendicular Lines and Planes 205
2. Parallel Lines and Planes 213
3. The Limiting Surface 219
4. Angle of Parallelism Formula 227
5. Triangle Relations 232
6. The Three Geometries 239
VII THE WEIERSTRASS MODEL 247
1. Preliminaries 248
2. H2 253
3. Distance in H2 257
4. Parametric Equation of a Line 262
5. Angles 265
6. The Homogeneous Representation 269
CONTENTS xi
7. Parallels and Horocycles 270
8. Intersections 274
9. Equidistant Curves 275
VIII LOBACHEVSKIAN GEOMETRY AND PHYSICAL
SPACE 279
1. Defects and the Parallax of Stars 280
2. The Finite Curved Universe 283
3. Philosophical Objections:
Truth or Convenience 288
APPENDIX A: Definitions, Postulates, Propositions of Euclid,
Book I 291
APPENDIX B: Hilbert's Postulates 299
APPENDIX C: Hyperbolic Functions 309
APPENDIX D: Vector Geometry and Analysis 313
BIBLIOGRAPHY 321
INDEX 325 |
| any_adam_object | 1 |
| author | Faber, Richard L. 1940- |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 512f MAT 510f |
| ctrlnum | (OCoLC)8953706 (DE-599)BVBBV003637423 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-09-23T14:17:26Z |
| institution | BVB |
| isbn | 0824717481 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002317414 |
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| physical | xi, 329 Seiten Illustrationen |
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| publishDate | 1983 |
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| publisher | Dekker |
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| spelling | Faber, Richard L. 1940- (DE-588)1144413400 aut Foundations of Euclidean and non-Euclidean geometry Richard L. Faber New York, [New York], [u.a.] Dekker 1983 xi, 329 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 73 Euclidische meetkunde gtt Exercice géométrie Formule Weierstrass Géométrie Géométrie Lobacevskij Géométrie non euclidienne ram Géométrie non-euclidienne Géométrie ram Histoire géométrie Geometry Geometry, Non-Euclidean Grundlage (DE-588)4158388-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf Nichteuklidische Geometrie (DE-588)4042073-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Nichteuklidische Geometrie (DE-588)4042073-5 s DE-604 Euklidische Geometrie (DE-588)4137555-5 s Geometrie (DE-588)4020236-7 s Grundlage (DE-588)4158388-7 s Pure and applied mathematics 73 (DE-604)BV000001885 73 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002317414&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faber, Richard L. 1940- Foundations of Euclidean and non-Euclidean geometry Pure and applied mathematics Euclidische meetkunde gtt Exercice géométrie Formule Weierstrass Géométrie Géométrie Lobacevskij Géométrie non euclidienne ram Géométrie non-euclidienne Géométrie ram Histoire géométrie Geometry Geometry, Non-Euclidean Grundlage (DE-588)4158388-7 gnd Geometrie (DE-588)4020236-7 gnd Euklidische Geometrie (DE-588)4137555-5 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| subject_GND | (DE-588)4158388-7 (DE-588)4020236-7 (DE-588)4137555-5 (DE-588)4042073-5 (DE-588)4151278-9 |
| title | Foundations of Euclidean and non-Euclidean geometry |
| title_auth | Foundations of Euclidean and non-Euclidean geometry |
| title_exact_search | Foundations of Euclidean and non-Euclidean geometry |
| title_full | Foundations of Euclidean and non-Euclidean geometry Richard L. Faber |
| title_fullStr | Foundations of Euclidean and non-Euclidean geometry Richard L. Faber |
| title_full_unstemmed | Foundations of Euclidean and non-Euclidean geometry Richard L. Faber |
| title_short | Foundations of Euclidean and non-Euclidean geometry |
| title_sort | foundations of euclidean and non euclidean geometry |
| topic | Euclidische meetkunde gtt Exercice géométrie Formule Weierstrass Géométrie Géométrie Lobacevskij Géométrie non euclidienne ram Géométrie non-euclidienne Géométrie ram Histoire géométrie Geometry Geometry, Non-Euclidean Grundlage (DE-588)4158388-7 gnd Geometrie (DE-588)4020236-7 gnd Euklidische Geometrie (DE-588)4137555-5 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| topic_facet | Euclidische meetkunde Exercice géométrie Formule Weierstrass Géométrie Géométrie Lobacevskij Géométrie non euclidienne Géométrie non-euclidienne Histoire géométrie Geometry Geometry, Non-Euclidean Grundlage Geometrie Euklidische Geometrie Nichteuklidische Geometrie Einführung |
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