아폴로니우스 원 패킹의 대화식 시각화 = Interactive visualization of Apollonian circle packings

다국어 초록 (Multilingual Abstract)

A Descartes configuration is a configuration of four circles where each circle is tangent to the other three. The Descartes Circle Theorem says that in the Descartes configuration of four mutually tangent circles, the curvatures satisfy. k21+k22+k23+k24=½ (k1 +k2+k3+k4)² An Apollonian circle packings are infinite packings of circles constructed recursively from an initial Descartes configuration of four mutually tangent circles externally tangent to triples of such circles. We can easily construct a circle externally tangent to each of three mutually tangent circles using the Descartes Circle Theorem. The purpose of this work is to create interactive circle packings movies using Adobe Flash drawing API that provide the opportunity for students to easily explore Descartes configurations and Apollonian circle packings, This work also consider Beecroft`s proof of the Descartes circle theorem.