Abstract
In this paper, I want to present to the readers some basic
knowledge about circle packing in the setting of Euclidean plane.
Circle packing was introduced by William Thurston [8] in his
lecture notes. I will establish the background on the discrete
analytic function, which maps carriers of circle packings to
carriers of circle packings and preserve the orientation and
tangency. Last, I will present the proof of the Thurston's
Conjecture on circle packings, which was proved by Burton Rodin and
Dennis Sullivan [5], and is now called the Rodin-Sullivan
Theorem.
Table of Contents
Table of Contents
1. Introduction...1
2. Introduction to Circle Packing...2
3. Conformal and Quasiconformal Mappings...12
4. Lemmas for the Main Theorem...21
5. Rodin-Sullivan Theorem...28
6. Reference...34
About this Honors Thesis
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