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Geometry of Continued Fractions on Hardback by Oleg N. Karpenkov
Geometry of Continued Fractions on Hardback by Oleg N. Karpenkov
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Geometry of Continued Fractions

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Description

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.

Author Biography:

Oleg Karpenkov is a mathematician at the University of Liverpool (UK), working in the general area of discrete geometry and its applications. More specifically, his research interests include geometry of numbers, discrete and semi-discrete differential geometry and self-stressed configurations of graphs. Oleg has completed his Ph.D. at Moscow State University under the supervision of Vladimir Arnold in 2005. Further he held several postdoctoral positions in Paris (Fellowship of the Mairie de Paris), Leiden, and Graz (Lise Meitner Fellowship) before arriving in Liverpool in 2012. In 2013 he published a book "Geometry of Continued Fractions" (its extended second edition will be available soon). Currently his Erdos number is 3.
Release date NZ
May 29th, 2022
Audience
  • Professional & Vocational
Edition
2nd ed. 2022
Illustrations
69 Illustrations, black and white; XX, 451 p. 69 illus.
Pages
451
ISBN-13
9783662652763
Product ID
35842866

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