Geometry of Continued Fractions

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Geometry of Continued Fractions by Oleg Karpenkov, Springer Berlin Heidelberg
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Author: Oleg Karpenkov ISBN: 9783642393686
Publisher: Springer Berlin Heidelberg Publication: August 15, 2013
Imprint: Springer Language: English
Author: Oleg Karpenkov
ISBN: 9783642393686
Publisher: Springer Berlin Heidelberg
Publication: August 15, 2013
Imprint: Springer
Language: English

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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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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