Geometry from a differentiable viewpoint:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1994
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 308 S. Ill., graph. Darst. |
| ISBN: | 052141430X 0521424801 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometry from a differentiable viewpoint |c John McCleary |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1994 | |
| 300 | |a XII, 308 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Geometrie - Geschichte | |
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Record in the Search Index
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| adam_text | Contents
Introduction page ix
PART A
Prelude and themes: Synthetic methods and results
1. Spherical geometry 3
2. Euclid 10
Euclid s theory of parallels 16
Appendix. The Elements: Book I 21
3. The theory of parallels 24
Uniqueness of parallels 24
Equidistance and boundedness of parallels 26
On the angle sum of a triangle 28
Similarity of triangles 31
4. Non Euclidean geometry I 34
The work of Saccheri 34
The work of Gauss, Bolyai, and Lobachevskil 39
5. Non Euclidean geometry II 45
The circumference of a circle 56
PART B
Development: Differential geometry
6. Curves 63
Early work on plane curves (Huygens, Leibniz, Newton, Euler) 66
The tractrix 69
Directed curvature 70
Digression: Involutes and evolutes 72
7. Curves in space 80
Appendix: On Euclidean rigid motions 89
8. Surfaces 95
The tangent plane 101
The first fundamental form 106
Area 112
8Ws. Map projections 116
Stereographic projection 120
vii
viii Contents
Central projection 123
Mercator projection 124
Lambert s cylindrical projection 126
Azimuthal projection 126
Sample map projections 127
9. Curvature for surfaces 131
Euler s work on surfaces 131
The Gauss map 134
10. Metric equivalence of surfaces 145
Special coordinates 151
11. Geodesies 157
Euclid revisited I: The Hopf Rinow theorem 165
12. The Gauss Bonnet theorem 171
Euclid revisited II: Uniqueness of lines 175
Compact surfaces 176
A digression on curves 180
13. Constant curvature surfaces 186
Euclid revisited III: Congruences 191
The work of Minding 192
PART C
Recapitulation and coda
14. Abstract surfaces 201
Hilbert s theorem 203
Abstract surfaces 206
15. Modeling the non Euclidean plane 217
The Beltrami disk 220
The Poincare disk 224
The Poincare half plane 227
16. Epilog: Where from here? 242
Manifolds (differential topology) 243
Vector and tensor fields 247
Metrical relations (Riemannian manifolds) 249
Curvature 252
Covariant differentiation 261
Riemann s Habilitationsvortrag: On the hypotheses which lie at the foundations
of geometry 269
Appendix: Notes on selected exercises 279
Bibliography 297
Symbol index 303
Name index 304
Subject index 305
|
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| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516.36 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| genre | Lehrbuch - Differentialgeometrie |
| genre_facet | Lehrbuch - Differentialgeometrie |
| id | DE-604.BV010279699 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:49:46Z |
| institution | BVB |
| isbn | 052141430X 0521424801 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006839869 |
| oclc_num | 612792474 |
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| physical | XII, 308 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | McCleary, John 1952- Verfasser (DE-588)113779089 aut Geometry from a differentiable viewpoint John McCleary 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1994 XII, 308 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometrie - Geschichte Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Lehrbuch - Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006839869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McCleary, John 1952- Geometry from a differentiable viewpoint Geometrie - Geschichte Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | Geometry from a differentiable viewpoint |
| title_auth | Geometry from a differentiable viewpoint |
| title_exact_search | Geometry from a differentiable viewpoint |
| title_full | Geometry from a differentiable viewpoint John McCleary |
| title_fullStr | Geometry from a differentiable viewpoint John McCleary |
| title_full_unstemmed | Geometry from a differentiable viewpoint John McCleary |
| title_short | Geometry from a differentiable viewpoint |
| title_sort | geometry from a differentiable viewpoint |
| topic | Geometrie - Geschichte Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometrie - Geschichte Differentialgeometrie Lehrbuch - Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006839869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mcclearyjohn geometryfromadifferentiableviewpoint |