Fields Institute Monographs

Lectures on Sphere Arrangements – the Discrete Geometric Side

Authors: Bezdek, Károly

  • ​Contains more than 40 open research problems proposed to help further research
  • Ideal for graduate students as well as researchers in mathematics and computer science
  • Acts as a short introduction to important and modern parts of discrete geometry
  • Ideal book for a one semester course at an advanced undergraduate or graduate level course
  • Features proofs that cover a broad range of methods of discrete geometry, often presentable in short talks
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eBook $84.99
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  • ISBN 978-1-4614-8118-8
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  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4614-8117-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4939-0032-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
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About this book

This 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.

Reviews

From 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)


Table of contents (9 chapters)

  • Unit Sphere Packings

    Bezdek, Károly

    Pages 1-16

  • Proofs on Unit Sphere Packings

    Bezdek, Károly

    Pages 17-56

  • Contractions of Sphere Arrangements

    Bezdek, Károly

    Pages 57-66

  • Proofs on Contractions of Sphere Arrangements

    Bezdek, Károly

    Pages 67-81

  • Ball-Polyhedra and Spindle Convex Bodies

    Bezdek, Károly

    Pages 83-98

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-1-4614-8118-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4614-8117-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4939-0032-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Sphere Arrangements – the Discrete Geometric Side
Authors
Series Title
Fields Institute Monographs
Series Volume
32
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-1-4614-8118-8
DOI
10.1007/978-1-4614-8118-8
Hardcover ISBN
978-1-4614-8117-1
Softcover ISBN
978-1-4939-0032-9
Series ISSN
1069-5273
Edition Number
1
Number of Pages
XII, 175
Topics