A class of Cantor sets associated with the regular continued fractions

In this paper, we introduce a class of Cantor sets, which can be put into a one-to-one correspondence with the continued fraction expansions of irrational numbers. By using the recursive relations of the continued fractions, we get the exact Hausdorff dimensions of the Cantor sets. As an example, we exhibit a sequence of sets whose Hausdorff dimensions are an elementary function of the Fibonacci number.