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Packing up to 200 Equal Circles in a Square

  • Péter Gábor Szabó
  • Eckard Specht
Part of the Optimization and Its Applications book series (SOIA, volume 4)

Abstract

The Hungarian mathematician Farkas Bolyai (1775–1856) published in his principal work (‘Tentamen’, 1832–33 [Bol04]) a dense regular packing of equal circles in an equilateral triangle (see Fig. 1). He defined an infinite packing series and investigated the limit of vacuitas (in Latin, the gap in the triangle outside the circles). It is interesting that these packings are not always optimal in spite of the fact that they are based on hexagonal grid packings. Bolyai probably was the first author in the mathematical literature who studied the density of a series of packing circles in a bounded shape.

Keywords

Interval Arithmetic Global Optimization Problem Optimal Packing Circle Packing Improve Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Péter Gábor Szabó
    • 1
  • Eckard Specht
    • 2
  1. 1.Department of Applied InformaticsUniversity of SzegedSzegedHungary
  2. 2.Department of Experimental PhysicsUniversity of MagdeburgMagdeburgGermany

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