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. "
General
| Imprint: |
Springer-Verlag New York
|
| Country of origin: |
United States |
| Series: |
Fields Institute Monographs, 32 |
| Release date: |
August 2013 |
| First published: |
2013 |
| Authors: |
Karoly Bezdek
|
| Dimensions: |
235 x 155 x 15mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
175 |
| Edition: |
2013 ed. |
| ISBN-13: |
978-1-4614-8117-1 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
General
Promotions
|
| LSN: |
1-4614-8117-1 |
| Barcode: |
9781461481171 |
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