THE ASYMPTOTICS OF THE NUMBER OF DISCS IN APOLLONIAN PACKING

Authors

A.H. ARAKELYAN National Polytechnic University of Armenia Author

Keywords:

Apollonian gasket, packing of circles, Hausdorf dimension

Abstract

An Apollonian gasket is an elegant packing of tangent circles is constructed by repeatedly inscribing circles into the triangular interstices in configurations of four mutually tangent circles. For a fixed gasket, a natural quesstion arises, how quickly do the circles shrink, or alternatively, how many circles are there with bounded curvatures. An asymptotic result for this number is proposed.

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Published

17.07.2026

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