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).In this paper we prove Thurston's conjecture that his scheme converges to the Riemann mapping. Our proof uses a compactness property of circle packings, a length-area inequality for packings, and an approximate rigidity result about large pieces of the regular hexagonal packing ( §3 and Appendix FIGURE 1.1. An approximate conformal mapping

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rated the instructor slightly better on 8 dimensions than did those with a low social value orientation. The instructor was seen as more self-reliant and confident by the students with a low religious value orientation than by those with a high religious value orientation.-Purdue University. 0 100-09/SBR

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