Geometry of Continued Fractions

By: Oleg N. Karpenkov

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Hardcover | 29 May 2022 | Edition Number 2

At a Glance

Hardcover
472 Pages

Edition Type
Revised

Dimensions(cm)
16.0 x 24.0 x 3.4

Hardcover

$119.00

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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 approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects.

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.

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.

Industry Reviews

"There are a modest number of exercises at the end of each chapter; most of these are to work out specific numerical examples. I view this as a monograph on a very specialized subject rather than a textbook." (Allen Stenger, MAA Reviews, October 30, 2022)

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