By Doug Hensley

The Euclidean set of rules is among the oldest in arithmetic, whereas the examine of persevered fractions as instruments of approximation is going again at the very least to Euler and Legendre. whereas our realizing of persisted fractions and similar equipment for simultaneous diophantine approximation has burgeoned over the process the prior decade and extra, a few of the effects haven't been introduced jointly in booklet shape. persevered fractions were studied from the viewpoint of quantity thought, complicated research, ergodic thought, dynamic techniques, research of algorithms, or even theoretical physics, which has additional complex the location. This booklet areas particular emphasis on endured fraction Cantor units and the Hausdorff measurement, algorithms and research of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. vast, appealing computer-generated pictures are offered, and the underlying algorithms are mentioned and made on hand.

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