Hyperbolic Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
1999
|
| Schriftenreihe: | Springer Undergraduate Mathematics Series
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; brief discussion of generalizations to higher dimensions; many new exercises. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape |
| Beschreibung: | 1 Online-Ressource (IX, 230 p) |
| ISBN: | 9781447139874 9781852331566 |
| ISSN: | 1615-2085 |
| DOI: | 10.1007/978-1-4471-3987-4 |
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Datensatz im Suchindex
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| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-3987-4 |
| format | Electronic eBook |
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| id | DE-604.BV042419397 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781447139874 9781852331566 |
| issn | 1615-2085 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854814 |
| oclc_num | 864104580 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (IX, 230 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer London |
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| series2 | Springer Undergraduate Mathematics Series |
| spelling | Anderson, James W. Verfasser aut Hyperbolic Geometry by James W. Anderson London Springer London 1999 1 Online-Ressource (IX, 230 p) txt rdacontent c rdamedia cr rdacarrier Springer Undergraduate Mathematics Series 1615-2085 The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; brief discussion of generalizations to higher dimensions; many new exercises. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape Mathematics Geometry Mathematics, general Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s 1\p DE-604 https://doi.org/10.1007/978-1-4471-3987-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, James W. Hyperbolic Geometry Mathematics Geometry Mathematics, general Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 |
| title | Hyperbolic Geometry |
| title_auth | Hyperbolic Geometry |
| title_exact_search | Hyperbolic Geometry |
| title_full | Hyperbolic Geometry by James W. Anderson |
| title_fullStr | Hyperbolic Geometry by James W. Anderson |
| title_full_unstemmed | Hyperbolic Geometry by James W. Anderson |
| title_short | Hyperbolic Geometry |
| title_sort | hyperbolic geometry |
| topic | Mathematics Geometry Mathematics, general Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Mathematics Geometry Mathematics, general Mathematik Hyperbolische Geometrie |
| url | https://doi.org/10.1007/978-1-4471-3987-4 |
| work_keys_str_mv | AT andersonjamesw hyperbolicgeometry |