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001 978-1-4614-8118-8
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008 130804s2013 xxu| s |||| 0|eng d
020 _a9781461481188
_9978-1-4614-8118-8
024 7 _a10.1007/978-1-4614-8118-8
_2doi
050 4 _aQA639.5-640.7
050 4 _aQA640.7-640.77
072 7 _aPBMW
_2bicssc
072 7 _aPBD
_2bicssc
072 7 _aMAT012020
_2bisacsh
072 7 _aMAT008000
_2bisacsh
082 0 4 _a516.1
_223
100 1 _aBezdek, Károly.
_eauthor.
245 1 0 _aLectures on Sphere Arrangements – the Discrete Geometric Side
_h[electronic resource] /
_cby Károly Bezdek.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXII, 175 p. 18 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFields Institute Monographs,
_x1069-5273 ;
_v32
505 0 _a1. Unit Sphere Packings -- 2. Proofs on Unit Sphere Packings -- 3. Contractions of Sphere Arrangements -- 4. Proofs on Contractions of Sphere Arrangements -- 5. Ball-Polyhedra and Spindle Convex Bodies -- 6. Proofs on Ball-Polyhedra and Spindle Convex Bodies -- 7. Coverings by Cylinders -- 8. Proofs on Coverings by Cylinders -- 9. Research Problems - an Overview -- Glossary -- References.
520 _aThis monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers.  It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.   The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders.  
650 0 _aMathematics.
650 0 _aDiscrete groups.
650 1 4 _aMathematics.
650 2 4 _aConvex and Discrete Geometry.
650 2 4 _aPolytopes.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461481171
830 0 _aFields Institute Monographs,
_x1069-5273 ;
_v32
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8118-8
912 _aZDB-2-SMA
999 _c96028
_d96028