# 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} }

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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#### References

SHOWING 1-10 OF 15 REFERENCES

Packing up to 50 Equal Circles in a Square

- Mathematics, Computer Science
- Discret. Comput. Geom.
- 1997

Improved Coverings of a Square with Six and Eight Equal Circles

- Mathematics, Computer Science
- Electron. J. Comb.
- 1996

Covering a Rectangle with Six and Seven Circles

- Computer Science, Mathematics
- Discret. Appl. Math.
- 2000

Dense packings of congruent circles in a circle

- Computer Science, Mathematics
- Discret. Math.
- 1998

Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach

- Computer Science
- TOMS
- 1983

Packing and covering with circles

- Ph.D. thesis, Universiteit Utrecht, the Netherlands
- 1997