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Published 1999 Revised 2011
\def \leftb{} \def \rightb{}
In this article we shall see that every whole number can be written as a continued fraction of the form
{k\over\displaystyle 1+ \leftb {\strut k\over \displaystyle 1+ \leftb {\strut k\over \displaystyle 1+ {\strut k\over \displaystyle 1+ ... }}\rightb}\rightb}.
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?