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[Algorithms and Computation in Mathematics] Geometry of Continued Fractions Volume 26 || Other Generalizations of Continued Fractions

✍ Scribed by Karpenkov, Oleg

Book ID
121646931
Publisher
Springer Berlin Heidelberg
Year
2013
Tongue
German
Weight
408 KB
Edition
2013
Category
Article
ISBN
3642393683

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✦ Synopsis

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 toΒ such areas asΒ Diophantine approximation, algebraic number theory, and toric geometry. Β  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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