A CONTINUED-FRACTION TITBIT

In 1812 Gauss, in a letter to Laplace, proposed without proof a formul a explaining the statistical regularity of continued fractions. There has since been speculation concerning the manner in which Gauss arrive d at this formula. In this article we present a plausible explanation, which at the same time gives an elementary proof of the full ergodic nature of the underlying dynamical system. The method seems to be of i nterest for other number-theoretic expansions.