The non-Euclidean revolution:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Boston [u.a.]
Birkhäuser
1987
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 269 S. graph. Darst. |
| ISBN: | 0817633111 3764333111 |
Staff View
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| 100 | 1 | |a Trudeau, Richard J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The non-Euclidean revolution |
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| 300 | |a XII, 269 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Preface vii
Introduction (H. S. M. Coxeter) xiii
Chapter 1 First Things 1
The Origin of Deductive Geometry 1
Material Axiomatic Systems 5
Logic 7
Proofs 12
A Simple Example of a Material Axiomatic System 15
Exercises 19
Notes 19
Chapter 2 Euclidean Geometry 22
How Big Is a Point? 23
Euclid s Primitive Terms 30
Euclid s Defined Terms (Part 1) 33
Sufficient for Each Day Is the Rigor Thereof 35
Euclid s Defined Terms (Part 2) 38
Euclid s Axioms 39
Theorems Proven Without Postulate 5 44
Theorems Proven With Postulate 5 86
Index to Euclidean Geometry 97
Exercises 99
Notes 102
Chapter 3 Geometry and the Diamond Theory of Truth 106
Kant s Distinctions 107
Synthetic A Priori Statements 110
Geometry as Synthetic A Priori 111
Kant s Doctrine of Space 113
The Diamond Theory of Truth 114
Notes 116
xi
xii Contents
Chapter 4 The Problem With Postulate 5 118
Poseidonios 119
Proof of Postulate 5, After Poseidonios 121
Metageometry 122
Evaluation of Poseidonios Reorganization 123
Overview of Later Attempts 126
So Near 131
An Experimental Test of Postulate 5 147
Exercises 150
Notes 153
Chapter 5 The Possibility of Non Euclidean Geometry 154
The Logical Possibility of Non Euclidean Geometry 155
The Founders of Non Euclidean Geometry 157
The Psychological Impossibility of Non Euclidean Geometry 159
Formal Axiomatic Systems 162
A Simple Example of a Formal Axiomatic System 164
How to Not Let the Pictures Bother You 168
Exercise 172
Notes 172
Chapter 6 Hyperbolic Geometry 173
Hyperbolic Geometry (Part 1) 177
Reconciliation With Common Sense 207
Hyperbolic Geometry (Part 2) 209
Glimpses 218
Exercises 229
Notes 230
Chapter 7 Consistency 232
Models 233
Poincare s Model 235
Can We Be Sure Euclidean Geometry Is Consistent? 244
Notes 247
Chapter 8 Geometry and the Story Theory of Truth 248
Kant Revisited 248
The Luneburg Blank Theory of Visual Space 251
The Diamond Theory in Decline 255
The Story Theory of Truth 256
Notes 259
Bibliography 261
Index 263
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T15:20:06Z |
| institution | BVB |
| isbn | 0817633111 3764333111 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000518658 |
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| physical | XII, 269 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Birkhäuser |
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| spelling | Trudeau, Richard J. Verfasser aut The non-Euclidean revolution Boston [u.a.] Birkhäuser 1987 XII, 269 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometria Nao Euclidiana larpcal Géométrie non-euclidienne géométrie euclidienne inriac géométrie hyperbolique inriac géométrie non euclidienne inriac histoire mathématiques inriac Geometry, Non-Euclidean Nichteuklidische Geometrie (DE-588)4042073-5 gnd rswk-swf Nichteuklidische Geometrie (DE-588)4042073-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000518658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Trudeau, Richard J. The non-Euclidean revolution Geometria Nao Euclidiana larpcal Géométrie non-euclidienne géométrie euclidienne inriac géométrie hyperbolique inriac géométrie non euclidienne inriac histoire mathématiques inriac Geometry, Non-Euclidean Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| subject_GND | (DE-588)4042073-5 |
| title | The non-Euclidean revolution |
| title_auth | The non-Euclidean revolution |
| title_exact_search | The non-Euclidean revolution |
| title_full | The non-Euclidean revolution |
| title_fullStr | The non-Euclidean revolution |
| title_full_unstemmed | The non-Euclidean revolution |
| title_short | The non-Euclidean revolution |
| title_sort | the non euclidean revolution |
| topic | Geometria Nao Euclidiana larpcal Géométrie non-euclidienne géométrie euclidienne inriac géométrie hyperbolique inriac géométrie non euclidienne inriac histoire mathématiques inriac Geometry, Non-Euclidean Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| topic_facet | Geometria Nao Euclidiana Géométrie non-euclidienne géométrie euclidienne géométrie hyperbolique géométrie non euclidienne histoire mathématiques Geometry, Non-Euclidean Nichteuklidische Geometrie |
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