Classical Topics in Discrete Geometry

AvKároly Bezdek

Häftad, Engelska, 2012

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Beskrivning

Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.

Produktinformation

Utgivningsdatum:2012-09-05
Mått:155 x 235 x 11 mm
Vikt:283 g
Format:Häftad
Språk:Engelska
Serie:CMS Books in Mathematics
Antal sidor:166
Förlag:Springer-Verlag New York Inc.
ISBN:9781461426202

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "The present volume actually surveys packing and covering problems in Euclidean space and close cousins. ... Bezdek ... surveys the state of the art, best results, and outstanding conjectures for a host of problems. ... Summing Up: Recommended. Academic audiences, upper-division undergraduates through researchers/faculty." (D. V. Feldman, Choice, Vol. 48 (5), January, 2011) "The book is intended for graduate students interested in discrete geometry. The book provides a road map to the state-of-the-art of several topics in discrete geometry. It can also serve as a textbook for a graduate level course or a seminar. Additionally, the book is extremely current, with many references to as late as 2009-2010 publications." (Alex Bogomolny, The Mathematical Association of America, August, 2010) "This very interesting monograph contains a selection of topics in discrete geometry, mainly those on which the author and his collaborators have worked. ... The many conjectures and problems to be found throughout the text will serve as an inspiration to many discrete geometers." (Konrad Swanepoel, Zentralblatt MATH, Vol. 1207, 2011)

Innehållsförteckning

Classical Topics Revisited.- Sphere Packings.- Finite Packings by Translates of Convex Bodies.- Coverings by Homothetic Bodies - Illumination and Related Topics.- Coverings by Planks and Cylinders.- On the Volume of Finite Arrangements of Spheres.- Ball-Polyhedra as Intersections of Congruent Balls.- Selected Proofs.- Selected Proofs on Sphere Packings.- Selected Proofs on Finite Packings of Translates of Convex Bodies.- Selected Proofs on Illumination and Related Topics.- Selected Proofs on Coverings by Planks and Cylinders.- Selected Proofs on the Kneser–Poulsen Conjecture.- Selected Proofs on Ball-Polyhedra.