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Beschreibung
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.
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.
Zusammenfassung

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: [...]

Inhaltsverzeichnis
¿1. 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.
Details
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
Artikel-ID: 105920912

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