Some observations on the distribution of values of continued fractions (Q916922)

If all elements \(a_ n\) of a continued fraction \(K\frac{a_ n}{1}\) lie in an element region \(E\) then the corresponding values of \(K\frac{a_ n}{1}\) lie in a limit region \(V(E)\), for example \(E=\{z:| z| \leq 1/4\}\) the Worpitzky circle and \(V(E)=\{w:| w| \leq 1/2\}\) the limit region. The authors consider the probability distribution of \(w\) in \(V(E)\) on the assumption that \(a_ n\) is distributed evenly in \(E\). Theorems are stated and proven for several classical choices of \(E\) and are supported by numerical evidence. The paper is very readable with only a couple of misprints.