F.1 Discussion:

In this appendix, we did not declare $k$. This is because Example 3.2.2 uses different values of $k$ for different examples, to try for a better approximation. As we ran the code, we declared $k$ when we declared $count1$ and $count2$. When we reran with a higher value of $k$, we only iterated for $a$ in range $(9,31)$. The outputs from the code we ran is found in the tables in the examples, alongside the representation as continued fractions, which were computed using an online tool .