我們知道阿波羅尼奧斯墊片的豪斯多夫維度等於那些圓成長速率的指數次方，而在這篇論文中，我們將討論如果將邊界放寬至扇形甚至多邊形，是否仍然有著相同的圓成長速率並且數值上地計算出來。在文末，也會提到如何將阿波羅尼奧斯墊片應用至自然現象。

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.

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