Conjecturally Optimal Coverings of an Equilateral Triangle with Up to 36 Equal Circles

@article{Nurmela2000ConjecturallyOC,
  title={Conjecturally Optimal Coverings of an Equilateral Triangle with Up to 36 Equal Circles},
  author={K. Nurmela},
  journal={Experimental Mathematics},
  year={2000},
  volume={9},
  pages={241 - 250}
}
  • K. Nurmela
  • Published 2000
  • Computer Science, Mathematics
  • Experimental Mathematics
This paper presents a computational method to find good, conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles. The algorithm consists of two nested levels: on the inner level the uncovered area of the triangle is minimized by a local optimization routine while the radius of the circles is kept constant. The radius is adapted on the outer level to find a locally optimal covering. Good coverings are obtained byapplying the algorithm repeatedly to random initial… Expand
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