Classical Topics in Discrete Geometry
About the author: Karoly Bezdek received his Dr.rer.nat.(1980) and Habilitation (1997) degrees in mathematics from the Eötvös Loránd University, in Budapest and his Candidate of Mathematical Sciences (1985) and Doctor of Mathematical Sciences (1994) degre
- PDF / 2,655,392 Bytes
- 171 Pages / 439.37 x 666.142 pts Page_size
- 30 Downloads / 305 Views
other titles published in this series, go to www.springer.com/series/4318
Károly Bezdek
Classical Topics in Discrete Geometry
Károly Bezdek Department of Mathematics and Statistics University of Calgary 2500 University Drive NW Calgary, Alberta, T2N 1N4 Canada [email protected]
Editors-in-Chief Rédacteurs-en-chef K. Dilcher K. Taylor Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, B3H 3J5 Canada [email protected]
The author was supported by the Canada Research Chair program as well as a Natural Sciences and Engineering Research Council of Canada Discovery Grant.
ISSN 1613-5237 ISBN 978-1-4419-0599-4 e-ISBN 978-1-4419-0600-7 DOI 10.1007/978-1-4419-0600-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010930515 M athematics Subject Classification (2010): 52A38, 52A40, 52B60, 52C17, 52C22
© Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
´ and our sons D´aniel, M´at´e, and M´ark To my wife Eva
Preface
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 mathematicians including H.S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T´oth (Hungary) led to the new and fast developing field called discrete geometry. One can briefly 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. Discrete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mathematics, including convex and combinatorial geometry, coding theory, calculus of variations, di
Data Loading...
