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
W.B. Jurkat
and A. Peyerimhoff
Universitat ULM (MNH), Abt. f. Mathematic I, 7900 Ulm (Donau), Oberer Eselsberg, Germany
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.