By William P. Thurston,Silvio Levy
This e-book develops many of the notable richness, attractiveness, and tool of geometry in and 3 dimensions, and the powerful connection of geometry with topology. Hyperbolic geometry is the superstar. a robust attempt has been made to exhibit not only denatured formal reasoning (definitions, theorems, and proofs), yet a dwelling feeling for the topic. there are numerous figures, examples, and workouts of various difficulty.
This e-book used to be the starting place of a grand scheme built by means of Thurston that's now coming to fruition. within the Nineteen Twenties and Nineteen Thirties the math of two-dimensional areas used to be formalized. It used to be Thurston's objective to do an identical for three-d areas. to do that, he needed to identify the robust connection of geometry to topology--the learn of qualitative questions on geometrical buildings. the writer created a brand new set of thoughts, 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 e-book is the fruits of 2 a long time of study and has turn into crucial and influential textual content within the box. Its content material additionally supplied the equipment had to remedy one in all 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 excellent study e-book that makes a seminal contribution to the examine literature. Thurston acquired the Fields Medal, the mathematical similar of the Nobel Prize, in 1982 for the intensity and originality of his contributions to arithmetic. In 1979 he was once presented the Alan T. Waterman Award, which acknowledges a good younger researcher in any box of technological know-how or engineering supported via the nationwide technological know-how Foundation.