$Geometry of continued fractions /$

Geometry of continued fractions /

Saved in:

Bibliographic Details
Author / Creator:	Karpenkov, Oleg, author.
Imprint:	Heidelberg : Springer, [2013] ©2013
Description:	1 online resource (xvii, 405 pages) : illustrations.
Language:	English
Series:	Algorithms and computation in mathematics, 1431-1550 ; volume 26 Algorithms and computation in mathematics ; volume 26.
Subject:	Continued fractions. Continued fractions.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/9852544

Hidden Bibliographic Details
ISBN:	9783642393686 (electronic bk.) 3642393683 (electronic bk.) 9783642393679
Notes:	Includes bibliographical references and index. Description based on online resource; title from PDF title page (SpringerLink, viewed September 25, 2013).
Summary:	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.
Standard no.:	10.1007/978-3-642-39368-6