Packing of Incongruent Circles on the Sphere |
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Authors: | August Florian |
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Affiliation: | Universit?t Salzburg, Austria, AT
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Abstract: | In this paper we provide an upper bound to the density of a packing of circles on the sphere, with radii selected from a given finite set. This bound is precise, e.g. for the system of incircles of Archimedean tilings (4, 4, n) with n ? 6. A generalisation to the weighted density of packing is applied to problems of solidity of a packing of circles. The simple concept of solidity was introduced by L. Fejes Toóth [6]. In particular, it is proved that the incircles of the faces of the Archimedean tilings (4,6,6), (4,6,8) and (4, 6, 10) form solid packings. (Received 21 August 2000; in revised form 21 March 2001) |
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Keywords: | 2000 Mathematics Subject Classification: 52C15 52A40 52C20 |
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