The cube: a window to convex and discrete geometry
This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important a...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Schriftenreihe: | Cambridge tracts in mathematics
168 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture |
| Beschreibung: | 1 Online-Ressource (x, 174 Seiten) |
| ISBN: | 9780511543173 |
| DOI: | 10.1017/CBO9780511543173 |
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| 520 | |a This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture | ||
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Datensatz im Suchindex
| _version_ | 1804176883978338304 |
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| any_adam_object | |
| author | Zong, Chuanming |
| author_GND | (DE-588)1055795553 |
| author_facet | Zong, Chuanming |
| author_role | aut |
| author_sort | Zong, Chuanming |
| author_variant | c z cz |
| building | Verbundindex |
| bvnumber | BV043941805 |
| classification_rvk | SK 380 |
| collection | ZDB-20-CBO |
| contents | Basic notation -- Cross sections -- Projections -- Inscribed simplices -- Triangulations -- 0/1 polytopes -- Minkowski's conjecture -- Furtwangler's conjecture -- Keller's conjecture |
| ctrlnum | (ZDB-20-CBO)CR9780511543173 (OCoLC)850699252 (DE-599)BVBBV043941805 |
| dewey-full | 516.08 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.08 |
| dewey-search | 516.08 |
| dewey-sort | 3516.08 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543173 |
| format | Electronic eBook |
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| id | DE-604.BV043941805 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511543173 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350775 |
| oclc_num | 850699252 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (x, 174 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Zong, Chuanming Verfasser (DE-588)1055795553 aut The cube a window to convex and discrete geometry Chuanming Zong The Cube-A Window to Convex & Discrete Geometry Cambridge Cambridge University Press 2006 1 Online-Ressource (x, 174 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 168 Basic notation -- Cross sections -- Projections -- Inscribed simplices -- Triangulations -- 0/1 polytopes -- Minkowski's conjecture -- Furtwangler's conjecture -- Keller's conjecture This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture Convex geometry Discrete geometry Diskrete Geometrie (DE-588)4130271-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 s DE-604 Diskrete Geometrie (DE-588)4130271-0 s Erscheint auch als Druck-Ausgabe 978-0-521-85535-8 https://doi.org/10.1017/CBO9780511543173 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Zong, Chuanming The cube a window to convex and discrete geometry Basic notation -- Cross sections -- Projections -- Inscribed simplices -- Triangulations -- 0/1 polytopes -- Minkowski's conjecture -- Furtwangler's conjecture -- Keller's conjecture Convex geometry Discrete geometry Diskrete Geometrie (DE-588)4130271-0 gnd Konvexe Geometrie (DE-588)4407260-0 gnd |
| subject_GND | (DE-588)4130271-0 (DE-588)4407260-0 |
| title | The cube a window to convex and discrete geometry |
| title_alt | The Cube-A Window to Convex & Discrete Geometry |
| title_auth | The cube a window to convex and discrete geometry |
| title_exact_search | The cube a window to convex and discrete geometry |
| title_full | The cube a window to convex and discrete geometry Chuanming Zong |
| title_fullStr | The cube a window to convex and discrete geometry Chuanming Zong |
| title_full_unstemmed | The cube a window to convex and discrete geometry Chuanming Zong |
| title_short | The cube |
| title_sort | the cube a window to convex and discrete geometry |
| title_sub | a window to convex and discrete geometry |
| topic | Convex geometry Discrete geometry Diskrete Geometrie (DE-588)4130271-0 gnd Konvexe Geometrie (DE-588)4407260-0 gnd |
| topic_facet | Convex geometry Discrete geometry Diskrete Geometrie Konvexe Geometrie |
| url | https://doi.org/10.1017/CBO9780511543173 |
| work_keys_str_mv | AT zongchuanming thecubeawindowtoconvexanddiscretegeometry AT zongchuanming thecubeawindowtoconvexdiscretegeometry |