  The Apollonian gasket is a well-studied circle packing. Important properties
of the packing, including the distribution of the circle radii, are governed by
its Hausdorff dimension. No closed form is currently known for the Hausdorff
dimension, and its computation is a special case of a more general and hard
problem: effective, rigorous estimates of dimension of a parabolic limit set.
In this paper we develop an efficient method for solving this problem which
allows us to compute the dimension of the gasket to 128 decimal places and
rigorously justify the error bounds. We expect our approach to generalise
easily to other parabolic fractals.
