International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 4, Pages 479-496
doi: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 W. B. Jurkat and A. Peyerimhoff. 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 δn−1, δn, δn+1 which are independent of x and n.