Packings of Unequal Circles in a Convex Set |
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| Authors: | Blind Blind |
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| Institution: | Mathematisches Institut B, Universit?t Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany blind@mathematik.uni-stuttgart.de, DE
Waldburgstrasse 88, D-70563 Stuttgart, Germany Roswitha.Blind@spd-online.de, DE
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| Abstract: |
Abstract. In the Euclidean plane let T be a convex set, and let K
1
, ..., K
n
be a family of n ≥ 2 circles packed into T . We show that the density of each such packing is smaller than , the density of the densest packing of equal circles in the plane, provided the radii of the circles are not too different.
This extends a result of G. Fejes Tóth, where T was a polygon with at most six sides. |
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| Keywords: | |
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