Notes on geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Berlin u.a.
Springer
2004
|
| Ausgabe: | Corr. 4. print. 2000, 2. print. 2004 |
| Schriftenreihe: | Universitext.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | VIII, 109 S. graph. Darst. |
| ISBN: | 354012053X 038712053X |
Internformat
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Datensatz im Suchindex
| _version_ | 1804134547752747008 |
|---|---|
| adam_text | VII
Contents
Introduction
Part I: Euclidean Geometry
The Linear Groups
The Relationship Between O(n) and GL(n,R)
Affine
Isometries of Rn
Isometries of R2
Isometries of R3
Some Subsets of R3
Finite Groups of isometries
The Platonic Solids
Duality
The Symmetry Groups of the Platonic Solids
Finite Groups of Rotations of R3
Crystals
Rotations and Quaternions
Problems
Part II: Projective Geometry
Homogeneous Co-ordinates
The Topology of P1 and P2
Duality
Projective Groups
The Cross-Ratio
Fixed Points of Projectivities
The Elliptic Plane
Conies
Diagonalization of Quadratic Forms
Polarity
Problems
Part III: Hyperbolic Geometry
The Parallel Axiom
The Beltrami (or projective) Model
Stereographic
The
The Local Metric
Areas
Trigonometry
Hyperbolic Trigonometry
Lines and Polarity
Isometries
Elliptic Trigonometry
Vili
Problems 102
Further Reading 105
List
Index 108
Notes
This book offers a concrete and accessible treatment of Euclide¬
an, projective, and hyperbolic geometry, with more stress on
topological aspects than is found in most textbooks. The au¬
thor s purpose is to introduce students to geometry on the ba¬
sis of elementary concepts in linear algebra, group theory, and
metric spaces, ant to deepen their understanding of these top¬
ics in the process. A large number of exercises and problems is
included, some of which introduce new topics.
|
| adam_txt |
VII
Contents
Introduction
Part I: Euclidean Geometry
The Linear Groups
The Relationship Between O(n) and GL(n,R)
Affine
Isometries of Rn
Isometries of R2
Isometries of R3
Some Subsets of R3
Finite Groups of isometries
The Platonic Solids
Duality
The Symmetry Groups of the Platonic Solids
Finite Groups of Rotations of R3
Crystals
Rotations and Quaternions
Problems
Part II: Projective Geometry
Homogeneous Co-ordinates
The Topology of P1 and P2
Duality
Projective Groups
The Cross-Ratio
Fixed Points of Projectivities
The Elliptic Plane
Conies
Diagonalization of Quadratic Forms
Polarity
Problems
Part III: Hyperbolic Geometry
The Parallel Axiom
The Beltrami (or projective) Model
Stereographic
The
The Local Metric
Areas
Trigonometry
Hyperbolic Trigonometry
Lines and Polarity
Isometries
Elliptic Trigonometry
Vili
Problems 102
Further Reading 105
List
Index 108
Notes
This book offers a concrete and accessible treatment of Euclide¬
an, projective, and hyperbolic geometry, with more stress on
topological aspects than is found in most textbooks. The au¬
thor's purpose is to introduce students to geometry on the ba¬
sis of elementary concepts in linear algebra, group theory, and
metric spaces, ant to deepen their understanding of these top¬
ics in the process. A large number of exercises and problems is
included, some of which introduce new topics. |
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| discipline_str_mv | Mathematik |
| edition | Corr. 4. print. 2000, 2. print. 2004 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T13:16:19Z |
| indexdate | 2024-07-09T20:26:21Z |
| institution | BVB |
| isbn | 354012053X 038712053X |
| language | Undetermined |
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| physical | VIII, 109 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
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| series2 | Universitext. |
| spelling | Rees, Elmer G. Verfasser aut Notes on geometry Corr. 4. print. 2000, 2. print. 2004 Berlin u.a. Springer 2004 VIII, 109 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext. Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s DE-604 Projektive Geometrie (DE-588)4047436-7 s Euklidische Geometrie (DE-588)4137555-5 s Geometrie (DE-588)4020236-7 s Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014162318&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014162318&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Rees, Elmer G. Notes on geometry Projektive Geometrie (DE-588)4047436-7 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Geometrie (DE-588)4020236-7 gnd Euklidische Geometrie (DE-588)4137555-5 gnd |
| subject_GND | (DE-588)4047436-7 (DE-588)4161041-6 (DE-588)4020236-7 (DE-588)4137555-5 |
| title | Notes on geometry |
| title_auth | Notes on geometry |
| title_exact_search | Notes on geometry |
| title_exact_search_txtP | Notes on geometry |
| title_full | Notes on geometry |
| title_fullStr | Notes on geometry |
| title_full_unstemmed | Notes on geometry |
| title_short | Notes on geometry |
| title_sort | notes on geometry |
| topic | Projektive Geometrie (DE-588)4047436-7 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Geometrie (DE-588)4020236-7 gnd Euklidische Geometrie (DE-588)4137555-5 gnd |
| topic_facet | Projektive Geometrie Hyperbolische Geometrie Geometrie Euklidische Geometrie |
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