New Approaches to Circle Packing in a Square

In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand. 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 regularities. This book summarizes results achieved in solving the circle packing problem over the past few years, providing the reader with a comprehensive view of both theoretical and computational achievements. Typically illustrations of problem solutions are shown, elegantly displaying the results obtained.

Beyond the theoretically challenging character of the problem, the solution methods developed in the book also have many practical applications.

Since the codes can be worked with directly, they will enable the reader to improve on them and solve problem instances that still remain challenging, or to use them as a starting point for solving related application problems.

• SOIA
• computational geometry
• geometry
• optimization
• patterns

From the reviews:

"The book under review gives a detailed survey on the achievements of the last years on the problem of finding densest packings … . The text is written in a very comprehensive and informative way, and all the numerical results on densities are impressively illustrated by many figures of ‘optimal’ packings. … will serve as an excellent source for everybody, expert on non-expert, who is interested in circle packing or, who is just interested in the hardness of an appealing problem in discrete geometry." (Martin Henk, Zentralblatt MATH, Vol. 1128 (6), 2008)

• University of Szeged, Hungary

  P. G. Szabó, T. Csendes

• Hungarian Academy of Sciences, Budapest, Hungary

  M. Cs. Markót

• Otto von Guericke University of Magdeburg, Germany

  E. Specht

• University of Almería, Spain

  L. G. Casado, I. García

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