Minkowski geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1996
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
v. 63 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 313-330) and indexes 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 non-Euclidean geometry in a finite number of dimensions that is different from elliptic and hyperbolic geometry (and from the Minkowskian geometry of spacetime). Here the linear structure is the same as the Euclidean one but distance is not "uniform" in all directions. Instead of the usual sphere in Euclidean space, the unit ball is a general symmetric convex set. Therefore, although the parallel axiom is valid, Pythagoras' theorem is not This book begins by presenting the topological properties of Minkowski spaces, including the existence and essential uniqueness of Haar measure, followed by the fundamental metric properties - the group of isometries, the existence of certain bases and the existence of the Lowner ellipsoid. This is followed by characterizations of Euclidean space among normed spaces and a full treatment of two-dimensional spaces. The three central chapters present the theory of area and volume in normed spaces. The author describes the fascinating geometric interplay among the isoperimetrix (the convex body which solves the isoperimetric problem), the unit ball and their duals, and the ways in which various roles of the ball in Euclidean space are divided among them. The next chapter deals with trigonometry in Minkowski spaces and the last one takes a brief look at a number of numerical parameters associated with a normed space, including J.J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Each chapter ends with a section of historical notes and the book ends with a list of 50 unsolved problems . Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis |
| Beschreibung: | 1 Online-Ressource (xvi, 346 p.) |
| ISBN: | 052140472X 1107088267 1107325846 9780521404723 9781107088269 9781107325845 |
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| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1996 | |
| 300 | |a 1 Online-Ressource (xvi, 346 p.) | ||
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v v. 63 | |
| 500 | |a Includes bibliographical references (p. 313-330) and indexes | ||
| 500 | |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 | ||
| 500 | |a Minkowski geometry is a non-Euclidean geometry in a finite number of dimensions that is different from elliptic and hyperbolic geometry (and from the Minkowskian geometry of spacetime). Here the linear structure is the same as the Euclidean one but distance is not "uniform" in all directions. Instead of the usual sphere in Euclidean space, the unit ball is a general symmetric convex set. Therefore, although the parallel axiom is valid, Pythagoras' theorem is not | ||
| 500 | |a This book begins by presenting the topological properties of Minkowski spaces, including the existence and essential uniqueness of Haar measure, followed by the fundamental metric properties - the group of isometries, the existence of certain bases and the existence of the Lowner ellipsoid. This is followed by characterizations of Euclidean space among normed spaces and a full treatment of two-dimensional spaces. The three central chapters present the theory of area and volume in normed spaces. The author describes the fascinating geometric interplay among the isoperimetrix (the convex body which solves the isoperimetric problem), the unit ball and their duals, and the ways in which various roles of the ball in Euclidean space are divided among them. The next chapter deals with trigonometry in Minkowski spaces and the last one takes a brief look at a number of numerical parameters associated with a normed space, including J.J. | ||
| 500 | |a Schaffer's ideas on the intrinsic geometry of the unit sphere. Each chapter ends with a section of historical notes and the book ends with a list of 50 unsolved problems | ||
| 500 | |a . Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis | ||
| 650 | 7 | |a Minkowski-ruimte |2 gtt | |
| 650 | 4 | |a Minkowski, Géométrie de | |
| 650 | 7 | |a Minkowski, Géométrie de |2 ram | |
| 650 | 7 | |a MATHEMATICS / Geometry / Analytic |2 bisacsh | |
| 650 | 7 | |a Minkowski geometry |2 fast | |
| 650 | 4 | |a Minkowski geometry | |
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Datensatz im Suchindex
| _version_ | 1804175492721410048 |
|---|---|
| any_adam_object | |
| author | Thompson, Anthony C. |
| author_facet | Thompson, Anthony C. |
| author_role | aut |
| author_sort | Thompson, Anthony C. |
| author_variant | a c t ac act |
| building | Verbundindex |
| bvnumber | BV043091391 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)852898451 (DE-599)BVBBV043091391 |
| 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 |
| format | Electronic eBook |
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| id | DE-604.BV043091391 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:09Z |
| institution | BVB |
| isbn | 052140472X 1107088267 1107325846 9780521404723 9781107088269 9781107325845 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028515583 |
| oclc_num | 852898451 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xvi, 346 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Thompson, Anthony C. Verfasser aut Minkowski geometry A.C. Thompson Cambridge Cambridge University Press 1996 1 Online-Ressource (xvi, 346 p.) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications v. 63 Includes bibliographical references (p. 313-330) and indexes 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 non-Euclidean geometry in a finite number of dimensions that is different from elliptic and hyperbolic geometry (and from the Minkowskian geometry of spacetime). Here the linear structure is the same as the Euclidean one but distance is not "uniform" in all directions. Instead of the usual sphere in Euclidean space, the unit ball is a general symmetric convex set. Therefore, although the parallel axiom is valid, Pythagoras' theorem is not This book begins by presenting the topological properties of Minkowski spaces, including the existence and essential uniqueness of Haar measure, followed by the fundamental metric properties - the group of isometries, the existence of certain bases and the existence of the Lowner ellipsoid. This is followed by characterizations of Euclidean space among normed spaces and a full treatment of two-dimensional spaces. The three central chapters present the theory of area and volume in normed spaces. The author describes the fascinating geometric interplay among the isoperimetrix (the convex body which solves the isoperimetric problem), the unit ball and their duals, and the ways in which various roles of the ball in Euclidean space are divided among them. The next chapter deals with trigonometry in Minkowski spaces and the last one takes a brief look at a number of numerical parameters associated with a normed space, including J.J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Each chapter ends with a section of historical notes and the book ends with a list of 50 unsolved problems . Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis Minkowski-ruimte gtt Minkowski, Géométrie de Minkowski, Géométrie de ram MATHEMATICS / Geometry / Analytic bisacsh Minkowski geometry fast Minkowski geometry Geometrie der Zahlen (DE-588)4227477-1 gnd rswk-swf Geometrie der Zahlen (DE-588)4227477-1 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569342 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Thompson, Anthony C. Minkowski geometry Minkowski-ruimte gtt Minkowski, Géométrie de Minkowski, Géométrie de ram MATHEMATICS / Geometry / Analytic bisacsh Minkowski geometry fast 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-ruimte gtt Minkowski, Géométrie de Minkowski, Géométrie de ram MATHEMATICS / Geometry / Analytic bisacsh Minkowski geometry fast Minkowski geometry Geometrie der Zahlen (DE-588)4227477-1 gnd |
| topic_facet | Minkowski-ruimte Minkowski, Géométrie de MATHEMATICS / Geometry / Analytic Minkowski geometry Geometrie der Zahlen |
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