International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 609-612
Short proofs of theorems of Lekkerkerker and Ballieu
Eberhardstr. 14, 79 Ulm/Donau, Germany
Received 16 October 1981
Copyright © 1982 Max Riederle. 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.
For any irrational number let denote the set of all accumulation points of . In this paper the following theorem of Lekkerkerker is proved in a short and elementary way: The set is discrete and does not contain zero if and only if is a quadratic irrational. The procedure used for this proof simultaneously takes care of a theorem of Ballieu.