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New approaches to circle packing in a square : with program codes

Author: P G Szabó
Publisher: New York : Springer, ©2007.
Series: Springer optimization and its applications, v. 6.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand: it is a matter of positioning a given number of equal circles in such a way that the circles fit fully in a square without overlapping. But on closer inspection, this problem reveals itself to be an interesting challenge of discrete and computational geometry with all its surprising structural forms and  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
New approaches to circle packing in a square.
New York : Springer, ©2007
(DLC) 2006932708
(OCoLC)123181404
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: P G Szabó
ISBN: 9780387456768 0387456767 0387456732 9780387456737
OCLC Number: 186565534
Description: 1 online resource (xiv, 238 pages) : illustrations.
Contents: Preface --
Glossary of Symbols --
1. Introduction and Problem History --
2. Problem Definitions and Formulations --
3. Bounds for the Optimum Values --
4. Approximate Circle Packings Using Optimization Methods --
5. Other Methods for Finding Approximate Circle Packings --
6. Interval Methods for Validating Optimal Solutions --
7. The First Fully Interval-based Optimization Method --
8. The Improved Version of the Interval Optimization Method --
9. Interval Methods for Verifying Structural Optimality --
10. Repeated Patterns in Circle Packings --
11. Minimal Polynomials of Point Arrangements --
12. About the Codes Used --
Appendix A. Currently Best Known Results for Packing Congruent Circles in a Square --
Bibliography --
Related Web Sites --
List of Figures --
List of Tables --
Index.
Series Title: Springer optimization and its applications, v. 6.
Responsibility: by P.G. Szábo [and others].
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Abstract:

This book presents an overview of recent results achieved in solving the circle packing problem. It provides the reader with a comprehensive view of both theoretical and computational achievements.  Read more...

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