Fractions of the period of the continued fraction expansion of quadratic integers

The elementary nature and simplicity of the theory of continued fractions is mostly well disguised in the literature. This makes one reluctant to quote sources when making a remark on the subject and seems to necessitate redeveloping the theory ab initio. That had best be done succinctly. That is done here and allows the retrieval of some amusing results on pattern in the period of the continued fraction expansion of quadratic integers.