Abstract
This thesis introduces some previous work on Apollonian circle packing regarding computations of its Hausdorff dimension. The Hausdorff dimension is known to be the exponent of a power law on the growth rate of circles as their sizes decrease. We study the circle packing in more general sectors and polygons. We also numerically compute the exponent of the corresponding power law. At the end of this thesis, we will mention some real-world application of Apollonian circle packing, and other related problems.