History
The circle packing theorem was first proved by Paul Koebe. William Thurston rediscovered the circle packing theorem, and noted that it followed from the work of E. M. Andreev. Thurston also proposed a scheme for using the circle packing theorem to obtain a homeomorphism of a simply connected proper subset of the plane onto the interior of the unit disk. The Thurston Conjecture for Circle Packings is his conjecture that the homeomorphism will converge to the Riemann mapping as the radii of the circles tend to zero. The Thurston Conjecture was later proved by Burton Rodin and Dennis Sullivan. This led to a flurry of research on extensions of the circle packing theorem, relations to conformal mappings, and applications.
Read more about this topic: Circle Packing Theorem
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