A051658 Experimental values for maximal number of contacts between equal circles and the box that are packed into a square.

4, 5, 7, 12, 12, 13, 14, 20, 24, 21, 20, 25, 25, 32, 36, 40, 34, 38, 37, 44, 39, 43, 56, 56, 60, 56, 55, 57, 65, 65, 55, 63, 65, 80, 80, 84, 77, 77, 80, 85, 100, 90, 85, 82, 94, 91, 94, 111, 120, 100, 97, 105, 110, 115, 113, 119, 113

Offset: 1

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.

Extensions

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