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International Journal of Mathematics and Mathematical Sciences
Volume 1, Issue 4, Pages 479-496
http://dx.doi.org/10.1155/S0161171278000472

Characteristic approximation properties of quadratic irrationals

Universitat ULM (MNH), Abt. f. Mathematic I, 7900 Ulm (Donau), Oberer Eselsberg, Germany

Received 19 April 1978

Copyright © 1978 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.

Abstract

Some characteristic approximation properties of quadratic irrationals are studied in this paper. It is shown that the limit points of the sequence δn form a subset C(x), and D(x) can be generated from C(x) in a relatively simple way. Another proof of Lekkerkerker's theorem is given using relations between δn1, δn, δn+1 which are independent of x and n.