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#

Introduction

This web page is a report on the research done by the author in
the summer of 1999. In general, it discusses families of
continued fractions, and specifically, it presents a method for
proving that the partial quotients of a family of continued
fractions come from the square root of a given function. The type
of families discussed are those that have the form
,
where the primitive period
length of the continued fraction for
grows linearly
with *x*_{i}, for some
,
or linearly with respect
to the logarithm of .
The report will culminate with
the investigation of two specific families, on which a method of
proof can be applied that verifies certain properties of the
families. Although there is such an emphasis on continued
fractions, no familiarity with them is assumed. For a more formal
report on this research, see [5].

*mcenter*

*2000-01-06*