| 000 | 02494nam a22003738i 4500 | ||
|---|---|---|---|
| 001 | CR9780511543173 | ||
| 003 | UkCbUP | ||
| 005 | 20200124160235.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr|||||||||||| | ||
| 008 | 090505s2006||||enk o ||1 0|eng|d | ||
| 020 | _a9780511543173 (ebook) | ||
| 020 | _z9780521855358 (hardback) | ||
| 040 |
_aUkCbUP _beng _erda _cUkCbUP |
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| 050 | 0 | 0 |
_aQA639.5 _b.Z64 2006 |
| 082 | 0 | 4 |
_a516.08 _222 |
| 100 | 1 |
_aZong, Chuanming, _eauthor. |
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| 245 | 1 | 4 |
_aThe cube : _ba window to convex and discrete geometry / _cChuanming Zong. |
| 246 | 3 | _aThe Cube-A Window to Convex & Discrete Geometry | |
| 264 | 1 |
_aCambridge : _bCambridge University Press, _c2006. |
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| 300 |
_a1 online resource (x, 174 pages) : _bdigital, PDF file(s). |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aCambridge tracts in mathematics ; _v168 |
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| 500 | _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). | ||
| 505 | 0 | _aBasic notation -- Cross sections -- Projections -- Inscribed simplices -- Triangulations -- 0/1 polytopes -- Minkowski's conjecture -- Furtwangler's conjecture -- Keller's conjecture. | |
| 520 | _aThis 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. | ||
| 650 | 0 | _aConvex geometry. | |
| 650 | 0 | _aDiscrete geometry. | |
| 776 | 0 | 8 |
_iPrint version: _z9780521855358 |
| 830 | 0 |
_aCambridge tracts in mathematics ; _v168. |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1017/CBO9780511543173 |
| 999 |
_c517974 _d517972 |
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