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Algorithms and Computation in Mathematics

Geometry of Continued Fractions

Authors: Karpenkov, Oleg

  • New approach to the geometry of numbers, very visual and algorithmic
  • Numerous illustrations and examples
  • Problems for each chapter
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eBook 51,16 €
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  • ISBN 978-3-642-39368-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-642-39367-9
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  • Usually dispatched within 3 to 5 business days.
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About this Textbook

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.

About the authors

For different subjects contributed to this book, the author was awarded a Fellowship of the City of Paris (France), a Lise Meitner Fellowship (Austria) and the Moscow Mathematical Society Prize (Russia).

Reviews

“Throughout the book many theorems are accompanied by constructive algorithms. Due to its rich content and connections to several parts of mathematics this volume will be of interest to graduate students and researchers not only in number theory and discrete geometry.” (C. Baxa, Monatshefte für Mathematik, Vo. 180, 2016)

“Karpenkov … begins with a distinctive treatment of continued fraction foundations emphasizing lattice geometry. One-dimensional continued fractions connect to two-dimensional lattices--very apt for illustration. … Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (10), June, 2014)

“The book is well written and is easy to read and navigate. … The book features a number of helpful illustrations and tables, a detailed index, and a large bibliography. This text is likely to become a valuable resource for researchers and students interested in discrete geometry and Diophantine approximations, as well as their rich interplay and many connections.” (Lenny Fukshansky, zbMATH, Vol. 1297, 2014)


Table of contents (23 chapters)

  • Classical Notions and Definitions

    Karpenkov, Oleg

    Pages 3-18

    Preview Buy Chapter 30,19 €
  • On Integer Geometry

    Karpenkov, Oleg

    Pages 19-31

    Preview Buy Chapter 30,19 €
  • Geometry of Regular Continued Fractions

    Karpenkov, Oleg

    Pages 33-39

    Preview Buy Chapter 30,19 €
  • Complete Invariant of Integer Angles

    Karpenkov, Oleg

    Pages 41-46

    Preview Buy Chapter 30,19 €
  • Integer Trigonometry for Integer Angles

    Karpenkov, Oleg

    Pages 47-55

    Preview Buy Chapter 30,19 €

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-642-39368-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-642-39367-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Continued Fractions
Authors
Series Title
Algorithms and Computation in Mathematics
Series Volume
26
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-39368-6
DOI
10.1007/978-3-642-39368-6
Hardcover ISBN
978-3-642-39367-9
Series ISSN
1431-1550
Edition Number
1
Number of Pages
XVII, 405
Topics