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OverviewThis monograph gives a short introduction to the relevant modern parts of 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 more than 40 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 part 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 core topics. The first two topics surround 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 of this book 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 and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders. Full Product DetailsAuthor: Károly BezdekPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 2013 Volume: 32 Dimensions: Width: 15.50cm , Height: 1.00cm , Length: 23.50cm Weight: 2.934kg ISBN: 9781493900329ISBN 10: 1493900323 Pages: 175 Publication Date: 26 August 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1. 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.ReviewsFrom the reviews: This is an exciting book aimed at graduate students and researchers as it contains a multitude of open problems after leading the reader to the research frontier. (Kelly J. Pearson, zbMATH, Vol. 1281, 2014) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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