Geometry of Minkowski space-time:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
[Berlin ; Heidelberg]
Springer
2011
|
| Series: | Springer briefs in physics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | VIII, 116 S. graph. Darst. 24 cm, 420 g |
| ISBN: | 9783642179761 3642179762 9783642179778 |
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Record in the Search Index
| _version_ | 1826921929213214720 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 HYPERBOLIC NUMBERS 3
2.1 THE GEOMETRY ASSOCIATED WITH COMPLEX NUMBERS 4
2.2 GENERALIZATION OF COMPLEX NUMBERS 8
2.2.1 DEFINITION OF THE MODULUS 12
2.3 LORENTZ TRANSFORMATIONS AND SPACE-TIME GEOMETRY 12 2.4 THE GEOMETRY
ASSOCIATED WITH HYPERBOLIC NUMBERS 15 2.4.1 HYPERBOLIC ROTATIONS AS
LORENTZ TRANSFORMATIONS 18 2.5 CONCLUSIONS 19
2.6 APPENDIX 20
2.6.1 CUBIC EQUATION AND INTRODUCTION OF COMPLEX NUMBERS 20
2.6.2 GEOMETRICAL AND CLASSICAL DEFINITION OF HYPERBOLIC ANGLES 21
REFERENCES 23
3 GEOMETRICAL REPRESENTATION OF HYPERBOLIC NUMBERS 25 3.1 INTRODUCTION
25
3.2 EXTENSION OF HYPERBOLIC EXPONENTIAL FUNCTION AND HYPERBOLIC POLAR
TRANSFORMATION 26
3.3 GEOMETRY IN THE HYPERBOLIC PLANE 27
REFERENCES 31
4 TRIGONOMETRY IN THE HYPERBOLIC (MINKOWSKI) PLANE 33 4.1 ANALYTICAL
FORMALIZATION OF EUCLIDEAN TRIGONOMETRY 33 4.1.1 COMPLEX NUMBERS
INVARIANTS IN EUCLIDEAN PLANE 33 4.2 HYPERBOLIC ROTATION INVARIANTS IN
MINKOWSKI PLANE 35
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011288184
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
4.3 EXTENSION OF HYPERBOLIC TRIGONOMETRIC FUNCTIONS 36
4.3.1 FJELSTAD'S EXTENSION OF HYPERBOLIC TRIGONOMETRIC FUNCTIONS 38
4.4 GONIOMETRY IN THE MINKOWSKI PLANE 41
4.5 TRIGONOMETRY IN THE MINKOWSKI PLANE 42
4.5.1 ANALYTICAL DEFINITIONS OF HYPERBOLIC TRIGONOMETRIC FUNCTIONS 42
4.5.2 TRIGONOMETRIC LAWS IN HYPERBOLIC PLANE 44
4.6 TRIANGLES IN HYPERBOLIC PLANE 50
4.6.1 THE TRIANGULAR PROPERTY 50
4.6.2 THE ELEMENTS IN A RIGHT-ANGLED TRIANGLE 51
4.6.3 SOLUTION OF HYPERBOLIC TRIANGLES 52
REFERENCES 55
5 EQUILATERAL HYPERBOLAS AND TRIANGLES IN THE HYPERBOLIC PLANE . . 57
5.1 THEOREMS ON EQUILATERAL HYPERBOLAS 57
5.2 TRIANGLE AND EQUILATERAL HYPERBOLAS 65
5.2.1 CIRCUMSCRIBED HYPERBOLA 65
5.2.2 INSCRIBED AND EX-INSCRIBED HYPERBOLAS 67
5.2.3 NUMERICAL EXAMPLES 71
REFERENCES 72
6 THE MOTIONS IN MINKOWSKI SPACE-TIME (TWIN PARADOX) 73
6.1 INERTIAL MOTIONS 74
6.2 INERTIAL AND UNIFORMLY ACCELERATED MOTIONS 77
6.2.1 UNIFORM AND UNIFORMLY ACCELERATED MOTIONS 80
6.2.2 UNIFORM MOTIONS JOINED BY UNIFORMLY ACCELERATED MOTIONS 82
6.2.3 REVERSED TRIANGLE INEQUALITY FOR CURVED LINES 83
6.2.4 THE MOST GENERAL UNIFORM AND ACCELERATED MOTIONS . . 85 6.3
NON-UNIFORMLY ACCELERATED MOTIONS 87
6.3.1 THE CURVES IN EUCLIDEAN PLANE 87
6.3.2 FORMALIZATION OF NON-UNIFORMLY ACCELERATED M O T I O N S . . 90
6.3.3 PROPER TIME IN NON-UNIFORMLY ACCELERATED M O T I O N S . . . 93
6.4 CONCLUSIONS 94
REFERENCES 95
7 SOME FINAL CONSIDERATIONS 97
REFERENCES 99
APPENDIX A 101
INDEX 113 |
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV039639109 |
| classification_rvk | UH 8200 |
| ctrlnum | (OCoLC)707330885 (DE-599)DNB1011288184 |
| dewey-full | 530.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.11 |
| dewey-search | 530.11 |
| dewey-sort | 3530.11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| isbn | 9783642179761 3642179762 9783642179778 |
| language | English |
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| spelling | Geometry of Minkowski space-time Francesco Catoni ... [Berlin ; Heidelberg] Springer 2011 VIII, 116 S. graph. Darst. 24 cm, 420 g txt rdacontent n rdamedia nc rdacarrier Springer briefs in physics Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Nichteuklidische Geometrie (DE-588)4042073-5 gnd rswk-swf Raum-Zeit (DE-588)4302626-6 s Nichteuklidische Geometrie (DE-588)4042073-5 s DE-604 Catoni, Francesco Sonstige oth Erscheint auch als Online-Ausgabe Geometry of Minkowski Space-Time X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3713513&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024489061&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4302626-6 (DE-588)4042073-5 |
| title | Geometry of Minkowski space-time |
| title_auth | Geometry of Minkowski space-time |
| title_exact_search | Geometry of Minkowski space-time |
| title_full | Geometry of Minkowski space-time Francesco Catoni ... |
| title_fullStr | Geometry of Minkowski space-time Francesco Catoni ... |
| title_full_unstemmed | Geometry of Minkowski space-time Francesco Catoni ... |
| title_short | Geometry of Minkowski space-time |
| title_sort | geometry of minkowski space time |
| topic | Raum-Zeit (DE-588)4302626-6 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| topic_facet | Raum-Zeit Nichteuklidische Geometrie |
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