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Geometry of
Continued Fractions (Algorithms and Computation in
Mathematics) |
PRODUCT
DETAILS: Author: Oleg
Karpenkov Language: English Publisher: Springer Publication Date: 23 Aug 2013 Dimensions: 2.4 x 15.4 x 23 cm Format: Hardcover Pages: 403 Condition: NEW Product_ID: C64BC9C675
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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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Książki
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