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.
General
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