Geometry of Continued Fractions (Hardcover, 2013 ed.)

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Algorithms and Computation in Mathematics, 26
Release date:	August 2013
First published:	2013
Authors:	Oleg Karpenkov
Dimensions:	235 x 155 x 28mm (L x W x T)
Format:	Hardcover
Pages:	405
Edition:	2013 ed.
ISBN-13:	978-3-642-39367-9
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-642-39367-5
Barcode:	9783642393679

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