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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 303-320

Approximation of irrationals

University of Wisconsin-Whitewater, Department of Mathematics and Computer Science, Whitewater 53190, Wisconsin, USA

Received 13 January 1984; Revised 10 February 1985

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF), and defines it as Generalized Euclidean Algorithm (abbr. GEA) to approximate irrationals.

This paper deals with approximation of irrationals of degree n=2,3,5. Though approximations of these irrationals in a variety of patterns are known, the results are new and practical, since there is used an algorithmic method.