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
Famous quotes containing the word history:
“Whenever we read the obscene stories, the voluptuous debaucheries, the cruel and torturous executions, the unrelenting vindictiveness, with which more than half the Bible is filled, it would be more consistent that we called it the word of a demon than the Word of God. It is a history of wickedness that has served to corrupt and brutalize mankind.”
—Thomas Paine (1737–1809)
“America is the only nation in history which miraculously has gone directly from barbarism to degeneration without the usual interval of civilization.”
—Georges Clemenceau (1841–1929)