Geometry and the imagination:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Providence, RI
American Math. Soc., Chelsea
1999
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 357 S. Ill. graph. Darst. |
| ISBN: | 0821819984 |
Staff View
MARC
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| 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 | ||
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| 650 | 7 | |a Nichteuklidische Geometrie |2 swd | |
| 650 | 4 | |a Geometry, Non-Euclidean | |
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Record in the Search Index
| _version_ | 1821765536675004416 |
|---|---|
| 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 |
| author_GND | (DE-588)11855090X (DE-588)124733905 |
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| 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 | 2025-01-20T11:03:22Z |
| institution | BVB |
| isbn | 0821819984 |
| language | English German |
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| physical | IX, 357 S. Ill. graph. Darst. |
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| publisher | American Math. Soc., Chelsea |
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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 Geometrie (DE-588)4020236-7 gnd rswk-swf Topologie (DE-588)4060425-1 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 Geometrie (DE-588)4020236-7 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4060425-1 (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 Geometrie (DE-588)4020236-7 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Nichteuklidische Geometrie Geometry, Non-Euclidean Geometrie Topologie 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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