Minkowski geometry /:
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 directio...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1996.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 63. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (xvi, 346 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 313-330) and indexes. |
| ISBN: | 9781107088269 1107088267 9781107325845 1107325846 |
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| 505 | 0 | |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 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 | ||
| 520 | 8 | |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. | |
| 520 | 8 | |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. | |
| 520 | 8 | |a . Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis. | |
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| 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 | (OCoLC)852898451 |
| dewey-full | 516.3/74 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/74 |
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| id | ZDB-4-EBA-ocn852898451 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:26Z |
| institution | BVB |
| isbn | 9781107088269 1107088267 9781107325845 1107325846 |
| language | English |
| oclc_num | 852898451 |
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| series | Encyclopedia of mathematics and its applications ; |
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| spelling | Thompson, Anthony C., 1937- https://id.oclc.org/worldcat/entity/E39PBJg8JVTkmthkGrWfKkqhHC http://id.loc.gov/authorities/names/n83133654 Minkowski geometry / A.C. Thompson. Cambridge ; New York : Cambridge University Press, 1996. 1 online resource (xvi, 346 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 63 Includes bibliographical references (pages 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. Print version record. Minkowski geometry. http://id.loc.gov/authorities/subjects/sh95008990 Géométrie de Minkowski. MATHEMATICS Geometry Analytic. bisacsh Minkowski geometry fast Geometrie gnd http://d-nb.info/gnd/4020236-7 Minkowski-Raum gnd http://d-nb.info/gnd/4293944-6 Minkowski-ruimte. gtt Minkowski, Géométrie de. ram has work: Minkowski geometry (Text) https://id.oclc.org/worldcat/entity/E39PCFxcp8JCWDwqGF9G4PywFq https://id.oclc.org/worldcat/ontology/hasWork Print version: Thompson, Anthony C., 1937- Minkowski geometry. Cambridge ; New York : Cambridge University Press, 1996 052140472X (DLC) 95046491 (OCoLC)33442682 Encyclopedia of mathematics and its applications ; v. 63. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569342 Volltext |
| spellingShingle | Thompson, Anthony C., 1937- Minkowski geometry / Encyclopedia of mathematics and its applications ; 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. http://id.loc.gov/authorities/subjects/sh95008990 Géométrie de Minkowski. MATHEMATICS Geometry Analytic. bisacsh Minkowski geometry fast Geometrie gnd http://d-nb.info/gnd/4020236-7 Minkowski-Raum gnd http://d-nb.info/gnd/4293944-6 Minkowski-ruimte. gtt Minkowski, Géométrie de. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh95008990 http://d-nb.info/gnd/4020236-7 http://d-nb.info/gnd/4293944-6 |
| 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. http://id.loc.gov/authorities/subjects/sh95008990 Géométrie de Minkowski. MATHEMATICS Geometry Analytic. bisacsh Minkowski geometry fast Geometrie gnd http://d-nb.info/gnd/4020236-7 Minkowski-Raum gnd http://d-nb.info/gnd/4293944-6 Minkowski-ruimte. gtt Minkowski, Géométrie de. ram |
| topic_facet | Minkowski geometry. Géométrie de Minkowski. MATHEMATICS Geometry Analytic. Minkowski geometry Geometrie Minkowski-Raum Minkowski-ruimte. Minkowski, Géométrie de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569342 |
| work_keys_str_mv | AT thompsonanthonyc minkowskigeometry |