Minkowski geometry:
Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric p...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1996
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 63 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xvi, 346 pages) |
| ISBN: | 9781107325845 |
| DOI: | 10.1017/CBO9781107325845 |
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| 100 | 1 | |a Thompson, Anthony C. |d 1937- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Minkowski geometry |c A.C. Thompson |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1996 | |
| 300 | |a 1 online resource (xvi, 346 pages) | ||
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 63 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a The algebraic properties of linear spaces and convex sets -- 1. Norms and norm topologies -- 2. Convex bodies -- 3. Comparisons and contrasts with Euclidean space -- 4. Two-dimensional Minkowski spaces -- 5. The concept of area and content -- 6. Special properties of the Holmes-Thompson definition -- 7. Special properties of the Busemann definition -- 8. Trigonometry -- 9. Various numerical parameters -- 10. Fifty problems | |
| 520 | |a Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis | ||
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Datensatz im Suchindex
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| author | Thompson, Anthony C. 1937- |
| author_facet | Thompson, Anthony C. 1937- |
| author_role | aut |
| author_sort | Thompson, Anthony C. 1937- |
| author_variant | a c t ac act |
| building | Verbundindex |
| bvnumber | BV043941702 |
| classification_rvk | SK 370 SK 380 |
| collection | ZDB-20-CBO |
| contents | The algebraic properties of linear spaces and convex sets -- 1. Norms and norm topologies -- 2. Convex bodies -- 3. Comparisons and contrasts with Euclidean space -- 4. Two-dimensional Minkowski spaces -- 5. The concept of area and content -- 6. Special properties of the Holmes-Thompson definition -- 7. Special properties of the Busemann definition -- 8. Trigonometry -- 9. Various numerical parameters -- 10. Fifty problems |
| ctrlnum | (ZDB-20-CBO)CR9781107325845 (OCoLC)992928433 (DE-599)BVBBV043941702 |
| dewey-full | 516.3/74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/74 |
| dewey-search | 516.3/74 |
| dewey-sort | 3516.3 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107325845 |
| format | Electronic eBook |
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| id | DE-604.BV043941702 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781107325845 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350672 |
| oclc_num | 992928433 |
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| physical | 1 online resource (xvi, 346 pages) |
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| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Cambridge University Press |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Thompson, Anthony C. 1937- Verfasser aut Minkowski geometry A.C. Thompson Cambridge Cambridge University Press 1996 1 online resource (xvi, 346 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 63 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The algebraic properties of linear spaces and convex sets -- 1. Norms and norm topologies -- 2. Convex bodies -- 3. Comparisons and contrasts with Euclidean space -- 4. Two-dimensional Minkowski spaces -- 5. The concept of area and content -- 6. Special properties of the Holmes-Thompson definition -- 7. Special properties of the Busemann definition -- 8. Trigonometry -- 9. Various numerical parameters -- 10. Fifty problems Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis Minkowski geometry Geometrie der Zahlen (DE-588)4227477-1 gnd rswk-swf Geometrie der Zahlen (DE-588)4227477-1 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-40472-3 https://doi.org/10.1017/CBO9781107325845 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Thompson, Anthony C. 1937- Minkowski geometry The algebraic properties of linear spaces and convex sets -- 1. Norms and norm topologies -- 2. Convex bodies -- 3. Comparisons and contrasts with Euclidean space -- 4. Two-dimensional Minkowski spaces -- 5. The concept of area and content -- 6. Special properties of the Holmes-Thompson definition -- 7. Special properties of the Busemann definition -- 8. Trigonometry -- 9. Various numerical parameters -- 10. Fifty problems Minkowski geometry Geometrie der Zahlen (DE-588)4227477-1 gnd |
| subject_GND | (DE-588)4227477-1 |
| title | Minkowski geometry |
| title_auth | Minkowski geometry |
| title_exact_search | Minkowski geometry |
| title_full | Minkowski geometry A.C. Thompson |
| title_fullStr | Minkowski geometry A.C. Thompson |
| title_full_unstemmed | Minkowski geometry A.C. Thompson |
| title_short | Minkowski geometry |
| title_sort | minkowski geometry |
| topic | Minkowski geometry Geometrie der Zahlen (DE-588)4227477-1 gnd |
| topic_facet | Minkowski geometry Geometrie der Zahlen |
| url | https://doi.org/10.1017/CBO9781107325845 |
| work_keys_str_mv | AT thompsonanthonyc minkowskigeometry |