A051661 Experimental values for number of circles in packing equal circles into a square for which there are no loose circles.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 25, 27, 30, 34, 35, 36, 37, 38, 39, 42, 52, 56, 67, 68, 77, 80, 86, 87, 99, 120, 137, 143, 150, 188

Offset: 0

Author

Eckard Specht (eckard.specht(AT)physik.uni-magdeburg.de)

Keywords

• nonn

References

• H. T. Croft, K. J. Falconer and R. K. Guy: Unsolved problems in geometry, Springer, New York, 1991.

Links

• D. Boll, Optimal Packing Of Circles And Spheres
• L. G. Casado, I. García, P. G. Szabó, and T. Csendes, Packing Equal Circles in a Square II. - New Results for up to 100 Circles Using the TAMSASS-PECS Algorithm, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 207-224.
• E. Friedman, Erich's Packing Center
• C. D. Maranas, C. A. Floudas and P. M. Pardalos, New results in the packing of equal circles in a square, Discrete Mathematics 142 (1995), p. 287-293.
• K. J. Nurmela and Patric R. J. Östergård, Packing up to 50 equal circles in a square, Discrete Comput. Geom. 18 (1997) 1, p. 111-120.
• E. Specht, www.packomania.com
• P. G. Szabó, Packing up to 100 circles in a square.
• P. G. Szabó, T. Csendes, L. G. Casado, and I. García, Packing Equal Circles in a Square I. - Problem Setting and Bounds for Optimal Solutions, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 191-206.

Crossrefs

Complement of A051660.

Extensions

I do not know how many of these values have been rigorously proved. - N. J. A. Sloane