Continued fractions

A continued fraction is an expression obtained by representing a number as the sum of its integer part and the reciprocal of another number, and then (recursively) writing this other number as a continued fraction. 

For example, the fraction 48/11, shown above, can be written as 4 + 4/11. The reciprocal of the fractional part, 4/11, is 11/4, which can be…