Improved Coverings of a Square with Six and Eight Equal Circles

  • J. B. M. Melissen
  • P. C. Schuur


In a recent article, Tarnai and Gáspár used computer simulations to find thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius.

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