Characteristic approximation properties of quadratic irrationals

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.