Geometry of Continued Fractions

Geometry of Continued Fractions
Author: Oleg Karpenkov
Publisher: Springer Science & Business Media
Total Pages: 409
Release: 2013-08-15
Genre: Mathematics
ISBN: 3642393683


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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.


Geometry of Continued Fractions
Language: en
Pages: 409
Authors: Oleg Karpenkov
Categories: Mathematics
Type: BOOK - Published: 2013-08-15 - Publisher: Springer Science & Business Media

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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
Geometry of Continued Fractions
Language: en
Pages: 462
Authors: Oleg N. Karpenkov
Categories: Mathematics
Type: BOOK - Published: 2022-05-28 - Publisher: Springer Nature

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This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximati
Continued Fractions
Language: en
Pages: 261
Authors: Doug Hensley
Categories: Mathematics
Type: BOOK - Published: 2006-03-01 - Publisher: World Scientific

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The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Le
History of Continued Fractions and Padé Approximants
Language: en
Pages: 556
Authors: Claude Brezinski
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great e
Continued Fractions
Language: en
Pages: 202
Authors: A. M. Rockett
Categories: Mathematics
Type: BOOK - Published: 1992-08-01 - Publisher: World Scientific

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This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of th