Geometry of Continued Fractions .Oleg Karpenkov
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Author: Oleg Karpenkov
Page Count: 405 pages
Published Date: 23 Aug 2013
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Publication Country: Berlin, Germany
Language: English
ISBN: 9783642393679
File size: 17 Mb
File Name: Geometry.of.Continued.Fractions.pdf
Download Link: Geometry of Continued Fractions
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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.
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Author: Oleg Karpenkov
Page Count: 405 pages
Published Date: 23 Aug 2013
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Publication Country: Berlin, Germany
Language: English
ISBN: 9783642393679
File size: 17 Mb
File Name: Geometry.of.Continued.Fractions.pdf
Download Link: Geometry of Continued Fractions
---------------------------------------------------------------
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.
Read online Geometry of Continued Fractions Buy and read online Geometry of Continued Fractions Download and read Geometry of Continued Fractions ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent Download to iPad/iPhone/iOS, B&N nook Geometry of Continued Fractions
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