Using **continued fractions** also provides a way to express an irrational number and to approximateitsvalue. Thisexpressionallowsustostudycertaininterestingproperties of an irrational number. For example, consider the irrational number p 2. At rst

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 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 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 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 Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available

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