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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.
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.
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
Includes supplementary material: [...]
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xii
175 S. |
| ISBN-13: | 9781461481171 |
| ISBN-10: | 1461481171 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Bezdek, Károly |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 15 mm |
| Von/Mit: | Károly Bezdek |
| Erscheinungsdatum: | 05.08.2013 |
| Gewicht: | 0,453 kg |
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