The convergence of circle packings to the Riemann mapping

Introduction. In his address, 3 "The Finite Riemann Mapping Theorem", Bill Thurston discussed his elementary approach to Andreev's theorem (see 2 below) and gave a provocative, constructive, geometric approach to the Riemann mapping theorem (see 3). The method is quite beautiful and easy to implement on a computer (see Appendix 2).