The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of the past decade and more, many of the results have not been brought together in book form. Continued fractions have been studied from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation. This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.
FREE Two-Day Shipping for Students. Learn more |
| |||||||||||||||
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Editorial Reviews
Review
The topics are well-researched and well presented. -- MAA Online Book Review
The book is well written and contains all significant advances in continued fractions over the past decade. The reviewer warmly recommends the book to all who have an interest in continued fractions. --Mathematical Reviews
The book is well written and contains all significant advances in continued fractions over the past decade. The reviewer warmly recommends the book to all who have an interest in continued fractions. --Mathematical Reviews
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
Key Phrases - Statistically Improbable Phrases (SIPs):
(learn more)
classical continued fraction expansion, shortest nonzero vector, bounded partial quotients, scaled errors, lattice reduction algorithm, fraction algorithm, quadratic irrational, simultaneous diophantine approximation, rational inputs, gcd algorithm, lattice basis, shortest vector, leading eigenvalue, integral basis, iterated function systems, continued fractions, algebraic integer, euclidean algorithm, continued fraction expansions, reduced basis, partition tree New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
classical continued fraction expansion, shortest nonzero vector, bounded partial quotients, scaled errors, lattice reduction algorithm, fraction algorithm, quadratic irrational, simultaneous diophantine approximation, rational inputs, gcd algorithm, lattice basis, shortest vector, leading eigenvalue, integral basis, iterated function systems, continued fractions, algebraic integer, euclidean algorithm, continued fraction expansions, reduced basis, partition tree New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
See all 11 books this book cites
1
book
cites this book:
- Continued Fractions: Analytic Theory and Applications (Encyclopedia of Mathematics and its Applications) by William B. Jones on page 217, and page 224
- Orthogonal Polynomials and Special Functions (CBMS-NSF Regional Conference Series in Applied Mathematics) by Richard Askey in Back Matter
- The Encyclopedia of Integer Sequences by N. J.A. Sloane on page 44
- Sequences, Discrepancies and Applications (Lecture Notes in Mathematics) by Michael Drmota in Back Matter
- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews in Back Matter
See all 11 books this book cites
- Number Theory for the Millennium II by Millennial Conference on Number Theory on page 175
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product).
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
