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Geometry of Continued Fractions by Oleg Karpenkov
Geometry of Continued Fractions by Oleg Karpenkov
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Geometry of Continued Fractions

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Geometry of Continued Fractions

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Description

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.

Author Biography:

For different subjects contributed to this book, the author was awarded a Fellowship of the City of Paris (France), a Lise Meitner Fellowship (Austria) and the Moscow Mathematical Society Prize (Russia).
Release date NZ
August 21st, 2015
Audience
  • Professional & Vocational
Country of Publication
Germany
Edition
Softcover reprint of the original 1st ed. 2013
Illustrations
XVII, 405 p.
Imprint
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Pages
405
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Dimensions
155x235x22
ISBN-13
9783642444241
Product ID
23909660

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