Geometry and the imagination:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
Providence, RI
American Math. Soc., Chelsea
1999
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 357 S. Ill. graph. Darst. |
| ISBN: | 0821819984 |
Internformat
MARC
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| 100 | 1 | |a Hilbert, David |d 1862-1943 |e Verfasser |0 (DE-588)11855090X |4 aut | |
| 240 | 1 | 0 | |a Anschauliche Geometrie |
| 245 | 1 | 0 | |a Geometry and the imagination |c D. Hilbert and S. Cohn-Vossen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc., Chelsea |c 1999 | |
| 300 | |a IX, 357 S. |b Ill. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Nichteuklidische Geometrie |2 swd | |
| 650 | 4 | |a Geometry, Non-Euclidean | |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Topologie |0 (DE-588)4060425-1 |D s |
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| 700 | 1 | |a Cohn-Vossen, Stefan |d 1902-1936 |e Verfasser |0 (DE-588)124733905 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804140516242096128 |
|---|---|
| adam_text | CONTENTS
Preface
...............................................
iii
Chapter I
THE SIMPLEST CURVES AND SURFACES
§ 1.
Plane Curves
...................................... 1
§ 2.
The Cylinder, the Cone, the Conic Sections and Their
Surfaces of Revolution
............................ 7
§ 3.
The Second-Order Surfaces
.......................... 12
§4.
The Thread Construction of the Ellipsoid, and Confocal
Quadrics
....................-----................ 19
APPENDICES TO CHAPTEH I
1.
The Pedal-Point Construction of the Conies.
........... 25
2.
The Directrices of the Conies
..................___.. 27
3.
The Movable Rod Model of the
Hyperboloid............ 29
Chapter II
REGULAR SYSTEMS OF POINTS
Plane Lattices
..................................... 32
Plane Lattices in the Theory of Numbers
............... 37
Lattices in Three and More than Three Dimensions
..... 44
Crystals as Regular Systems of Points
................. 52
Regular Systems of Points and Discontinuous Groups of
Motions
.........................................56
§ 10.
Plane Motions and their Composition
;
Classification of the
Discontinuous Groups of Motions in the Plane
....... 59
§ 11.
The Discontinuous Groups of Plane Motions with Infinite
Unit Cells
....................................... 64
§ 12.
The Crystallographic Groups of Motions in the Plane.
Regular Systems of Points and Pointers. Division of
the Plane into Congruent Cells
.................... 70
§ 13.
Crystallographic Classes and Groups of Motions in Space.
Groups and Systems of Points with Bilateral Symmetry
81
§ 14.
The Regular Polyhedra
............................. 89
Chapter
III
PROJECTIVE CONFIGURATIONS
§ 15.
Preliminary Remarks about Plane Configurations
....... 95
§ 16.
The Configurations (73) and (83)
..................... 98
§ 17.
The Configurations (93)
.............................102
§ 18.
Perspective, Ideal Elements, and the Principle of Duality
in the Plane
.....................................112
§ 19.
Ideal Elements and the Principle of Duality in Space.
Desargues
Theorem and the
Desargues
Configuration
(10.) ...........................................119
§ 20.
Comparison of Pascal s and
Desargues
Theorems
........128
§ 21.
Preliminary Remarks on Configurations in Space
........133
§ 22.
Reye s Configuration
................................134
§ 23.
Regular Polyhedra in Three and Four Dimensions, and
their Projections
.................................143
§ 24.
Enumerative Methods of Geometry
....................157
§ 25. Schläfli s
Double-Six
................................164
Chapter IV
DIFFERENTIAL GEOMETRY
§ 26.
Plane Curves
.............................„........172
§ 27.
Space Curves
......................................178
§ 28.
Curvature of Surfaces. Elliptic, Hyperbolic, and Parabolic
Points. Lines of Curvature and Asymptotic Lines. Um¬
bilical Points, Minimal Surfaces, Monkey Saddles
.....183
§ 29.
The Spherical Image and Gaussian Curvature
...........193
§ 30.
Developable Surfaces, Ruled Surfaces
.................204
§ 31.
The Twisting of Space Curves
........................211
§ 32.
Eleven Properties of the Sphere
......................215
§ 33.
Bendings Leaving a Surface Invariant.
................232
§ 34.
Elliptic Geometry
..................................235
§ 35.
Hyperbolic Geometry, and its Relation to Euclidean and to
Elliptic Geometry
................................242
§ 36. Stereographic
Projection and Circle-Preserving Trans¬
formations.
Poincaré s
Model of the Hyperbolic Plane
. 248
§ 37.
Methods of Mapping, Isometric, Area-Preserving, Geo¬
desic, Continuous and
Conformai
Mappings
..........260
§ 38.
Geometrical Function Theory. Riemann s Mapping Theo¬
rem.
Conformai
Mapping in Space
.................263
§ 39.
Conformai
Mappings of Curved Surfaces. Minimal Sur¬
faces. Plateau s Problem
..........................268
Chapter V
KINEMATICS
§ 40.
Linkages
..........................................272
§ 41.
Continuous Rigid Motions of Plane Figures.
........... .275
§ 42.
An Instrument for Constructing the Ellipse and its Roul¬
ettes
............................................283
§ 43.
Continuous Motions in Space
........................285
Chapter VI
TOPOLOGY
§ 44.
Polyhedra
.........................-----.___...-----290
§ 45.
Surfaces
..........................................295
§ 46.
One-Sided Surfaces
.................................302
§ 47.
The
Projective
Plane as a Closed Surface
..............313
§ 49.
Topological Mappings of a Surface onto Itself. Fixed
Points. Classes of Mappings. The Universal Covering
Surface of the Torus
..............................324
§ 50.
Conformai
Mapping of the Torus
.....................330
§ 51.
The Problem of Contiguous Regions, The Thread Problem,
and the Color Problem
............................333
APPENDICES TO CHAPTER VI
1.
The
Projective
Plane in Four-Dimensional Space
.......340
2.
The Euclidean Plane in Four-Dimensional Space
........ 341
Index
...........................................____.. 345
|
| any_adam_object | 1 |
| author | Hilbert, David 1862-1943 Cohn-Vossen, Stefan 1902-1936 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)41256151 (DE-599)BVBBV024515236 |
| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T22:01:13Z |
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| isbn | 0821819984 |
| language | English German |
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| physical | IX, 357 S. Ill. graph. Darst. |
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| spelling | Hilbert, David 1862-1943 Verfasser (DE-588)11855090X aut Anschauliche Geometrie Geometry and the imagination D. Hilbert and S. Cohn-Vossen 2. ed. Providence, RI American Math. Soc., Chelsea 1999 IX, 357 S. Ill. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nichteuklidische Geometrie swd Geometry, Non-Euclidean Topologie (DE-588)4060425-1 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Geometrie (DE-588)4020236-7 s Topologie (DE-588)4060425-1 s 2\p DE-604 DE-604 Cohn-Vossen, Stefan 1902-1936 Verfasser (DE-588)124733905 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018489361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hilbert, David 1862-1943 Cohn-Vossen, Stefan 1902-1936 Geometry and the imagination Nichteuklidische Geometrie swd Geometry, Non-Euclidean Topologie (DE-588)4060425-1 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4020236-7 (DE-588)4151278-9 |
| title | Geometry and the imagination |
| title_alt | Anschauliche Geometrie |
| title_auth | Geometry and the imagination |
| title_exact_search | Geometry and the imagination |
| title_full | Geometry and the imagination D. Hilbert and S. Cohn-Vossen |
| title_fullStr | Geometry and the imagination D. Hilbert and S. Cohn-Vossen |
| title_full_unstemmed | Geometry and the imagination D. Hilbert and S. Cohn-Vossen |
| title_short | Geometry and the imagination |
| title_sort | geometry and the imagination |
| topic | Nichteuklidische Geometrie swd Geometry, Non-Euclidean Topologie (DE-588)4060425-1 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Nichteuklidische Geometrie Geometry, Non-Euclidean Topologie Geometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018489361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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