Bibliography

[Bli66] G. Blind, Ebene Lagerungen von Kreisen, deren Radien nicht sehr verschieden sind, Ph.D. Thesis, Technische Hochschule, Stuttgart, (1966).

[Bli69] G. Blind, Unterdeckungen der Ebene durch Kreise, J. Reine Angew. 236, 145-173 (1969).

[BB02] G. Blind and R. Blind, Packings of Unequal Circles in a Convex Set, Discrete Comput. Geom. ,28, 115-119 (2002).

[Toth53] L. Fejes Toth, Lagerungen in der Ebene auf der Kugel und im Raum, Springer-Verlag, Berlin, 1953, 2nd edn 1972.

[Toth64] L. Fejes Toth, Regular Figures , Pergamon Press, Oxford, 1964.

[Toth72] L. Fejes Toth, Covering the plane with convex discs, Acta Math. Acad. Sci Hungar. 23, 263-270 (1972).

[Toth84] L. Fejes Toth, Compact Packing of Circles, Studia Sci. Math. Hungar. 19, 103-107 (1984).
The first paper to define compact. He proves that compact packings have density at least as large as that of the single species packing.

[Flo60] A. Florian, Ausfullung der Ebene durch Kreise, Rend. Circ. Mat. Palermo 9, 1-13 (1960).

[Flo63] A. Florian, Dichteste Packung inkongruenter Kreise Monatsh. Math. 67, 229-242 (1963).

[Flo67] A. Florian, Geometry of Circular Layering, Acta Mathematica Academiae Scientiarum Hungaricae 18, 341-358 (1967).
In german. Some bounds on packing densities.

[Hep00] A. Heppes, On the densest packing of discs of radius 1 and root 2-1 Studia Sci. Math. Hungar. 36, 433-454 (2000).
Proof that for r=0.414..., the densest packing is a compact packing.

[Hep03] A. Heppes, Some Densest Two-Size Disc Packings in the Plane, Discrete Comput. Geom. 30, 241-262 (2003).
Proof that for r=0.637, 0.533, 0.349, 0.280 ,0.154, the densest packing is a compact packing.

[HM60] A. Heppes and J. Molnar, Ujabb eredmenyek a diszkret geometriaban, Matematikai Lapok 11, 330-355 (1960).
In Hungarian. Contains pictures of compact packings for r=0.637, 0.533, 0.414, 0.349, 0.280, 0.154

[Ken04] T. Kennedy, Compact packings of the plane with two sizes of discs, Preprint (from arXiv.org). (2004).
Proves that there are only nine values of r<1 such that compact packings are possible using discs of radii 1 and r.

[LH93] C. N. Likos and C. L. Henley, Complex alloy phases for binary hard-disc mixtures Philos. Mag. B 68, 85-113 (1993).
A non-rigorous study of the optimal packing problem with the additional constraint that the relative number of small and large discs is fixed.

[Mol59] J. Molnar, Unterdeckung und Uberdeckung der Ebene durch Kreise Ann. Univ. Sci. Budapest , 2, 33-40 (1959).
Pictures of compact packings for r=0.637, 0.533, 0.414, 0.349, 0.280, 0.154

[Thu1892] A. Thue, Om Nogle Geometrisk Taltheoretiske Theoremer, Forhdl. Skand. Naturforsk. 14, 352-353 (1892).

[Thu10] A. Thue, Uber die dichteste Zusammenstellung von kongruenten Kreisen in der Ebene Christiania Vid. Selsk. Skr. 1, 3-9 (1910).