By William P. Thurston
This booklet develops the various amazing richness, good looks, and tool of geometry in and 3 dimensions, and the robust connection of geometry with topology. Hyperbolic geometry is the big name. a powerful attempt has been made to express not only denatured formal reasoning (definitions, theorems, and proofs), yet a residing feeling for the topic. there are numerous figures, examples, and routines of various difficulty.
This ebook used to be the foundation of a grand scheme built by way of Thurston that's now coming to fruition. within the Twenties and Thirties the math of two-dimensional areas used to be formalized. It used to be Thurston's objective to do an analogous for three-d areas. to do that, he needed to identify the robust connection of geometry to topology--the examine of qualitative questions on geometrical buildings. the writer created a brand new set of techniques, and the expression "Thurston-type geometry" has develop into a commonplace.
Three-Dimensional Geometry and Topology had its origins within the kind of notes for a graduate path the writer taught at Princeton collage among 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever asked them. ultimately, the mailing record grew to multiple thousand names. The publication is the fruits of 2 a long time of analysis and has develop into an important and influential textual content within the box. Its content material additionally supplied the tools had to remedy considered one of arithmetic' oldest unsolved problems--the Poincaré Conjecture.
In 2005 Thurston received the 1st AMS e-book Prize, for Three-dimensional Geometry and Topology. The prize acknowledges an exceptional examine ebook that makes a seminal contribution to the learn literature. Thurston bought the Fields Medal, the mathematical an identical of the Nobel Prize, in 1982 for the intensity and originality of his contributions to arithmetic. In 1979 he was once offered the Alan T. Waterman Award, which acknowledges an excellent younger researcher in any box of technological know-how or engineering supported via the nationwide technology Foundation.