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
050 0 0 _aQA639.5
_b.Z64 2006
082 0 4 _a516.08
_222
100 1 _aZong, Chuanming,
_eauthor.
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.
300 _a1 online resource (x, 174 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v168
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.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511543173
999 _c517974
_d517972