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Open Disk Packings of a Disk

Published online by Cambridge University Press:  20 November 2018

John B. Wilker
John B. Wilker*
Affiliation:
University of Toronto
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 395 - 415
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Coxeter, H. S. M., Introduction to Geometry. John Wiley and Sons, Inc., New York, 1963.Google Scholar
2. H. G. Eggleston, , On Closest packing by equilateral triangles. Proc. Camb. Phil. Soc, 49 (1955), 26-30.Google Scholar
3. Hurewiscz, W. and Wallman, H., Dimension Theory. Princeton University Press, Princeton, 1948.Google Scholar
4. Larman, D. G., On the exponent of convergence of a packing of spheres. Mathematika, 13 (1966), 57-59.Google Scholar
5. Melzak, Z. A., Infinite packings of disks. Canad. J. Math., 18 (1966), 838-852.Google Scholar
6. Mergelyan, S. N., Uniform approximations to functions of a complex variable. Amer. Math. 'Soc. Transi. No. 101 (1955), p. 21.Google Scholar
7. Saks, S., Theory of the Integral. (Monographie Matematyczne 7), Warsyawa- Lwow, 1937.Google Scholar
8. Wesler, O., An infinite packing theorem for spheres. Proc. Amer. Math. Soc, 11 (1966), 324-326.Google Scholar