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A new proof for the residual set dimension of the apollonian packing

Published online by Cambridge University Press:  24 October 2008

Claude Tricot
Claude Tricot
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Y4, Canada
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Abstract

Let (Dn) be the apollonian packing of a curvilinear triangle T, ρn the radius of Dn, E = T—U Dn the residual set, dim (E) its Hausdorff dimension. In this paper we give a new proof of the equality dim proved by Boyd [2]. Our technique is to construct a sequence of regular triangles covering E, and suitable measures μkcarried by E which allow us to apply a density theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 413 - 423
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

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