ABSTRACT
The powerful tool of continued fractions was systematically studied for the first time by Huygens in the seventeenth century. These fractions appear in a natural way by means of the Euclidean algorithm and may be used to construct the set of real numbers out of the set of rationals. With respect to approximation, continued fractions may be regarded as substitutes for Farey fractions. They provide best approximations in a rather quick and easy way.
