Share

Geometry of Continued Fractions

2013-08-15 Mathematics
Download Geometry of Continued Fractions PDF Online Free

Author :
Release : 2013-08-15
Genre : Mathematics
Kind : eBook
Book Rating : 683/5 ( reviews)

GET EBOOK


Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg Karpenkov. This book was released on 2013-08-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Continued Fractions

2022-05-28 Mathematics
Download Geometry of Continued Fractions PDF Online Free

Author :
Release : 2022-05-28
Genre : Mathematics
Kind : eBook
Book Rating : 773/5 ( reviews)

GET EBOOK


Book Synopsis Geometry of Continued Fractions by : Oleg N. Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg N. Karpenkov. This book was released on 2022-05-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continued Fractions

1992-08-01 Mathematics
Download Continued Fractions PDF Online Free

Author :
Release : 1992-08-01
Genre : Mathematics
Kind : eBook
Book Rating : 526/5 ( reviews)

GET EBOOK


Book Synopsis Continued Fractions by : A. M. Rockett

Download or read book Continued Fractions written by A. M. Rockett. This book was released on 1992-08-01. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.

Continued Fractions

2008 Mathematics
Download Continued Fractions PDF Online Free

Author :
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 074/5 ( reviews)

GET EBOOK


Book Synopsis Continued Fractions by : Lisa Lorentzen

Download or read book Continued Fractions written by Lisa Lorentzen. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Continued Fractions consists of two volumes -- Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given.This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.

The Soʹs Geometry of Continued Fractions

1974 Continued fractions
Download The Soʹs Geometry of Continued Fractions PDF Online Free

Author :
Release : 1974
Genre : Continued fractions
Kind : eBook
Book Rating : /5 ( reviews)

GET EBOOK


Book Synopsis The Soʹs Geometry of Continued Fractions by : Frances D'Ann Fuquay

Download or read book The Soʹs Geometry of Continued Fractions written by Frances D'Ann Fuquay. This book was released on 1974. Available in PDF, EPUB and Kindle. Book excerpt:

You may also like...