Geodesic
Open Disk Packings of a Disk
Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 395-415

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It is an old problem to find how a collection of congruent plane figures should be arranged without overlapping to cover the largest possible fraction of the plane or some region of the plane. If similar figures of arbitrary different sizes are permitted, Vitali's theorem ([7] p. 109) guarantees that packings which cover almost all points are possible. It is natural to study the diameters of figures used in such a packing and we will investigate this for the case of a closed disk packed with smaller open disks. 
Wilker, John B. Open Disk Packings of a Disk. Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 395-415. doi: 10.4153/CMB-1967-038-2
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     author = {Wilker, John B.},
     title = {Open {Disk} {Packings} of a {Disk}},
     journal = {Canadian mathematical bulletin},
     pages = {395--415},
     year = {1967},
     volume = {10},
     number = {3},
     doi = {10.4153/CMB-1967-038-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-038-2/}
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