bokomslag Geometry of Continued Fractions
Vetenskap & teknik

Geometry of Continued Fractions

Oleg N Karpenkov

Inbunden

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Andra format:

  • 451 sidor
  • 2022
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.
  • Författare: Oleg N Karpenkov
  • Format: Inbunden
  • ISBN: 9783662652763
  • Språk: Engelska
  • Antal sidor: 451
  • Utgivningsdatum: 2022-05-29
  • Förlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K