In this circle packing problem, the task is to determine the smallest circle for a given number of unit circles.
However, in the case of $n=15$, it is not clear to me how the $$\ 1+ \sqrt{6+ {2\over \sqrt{5}} +4 \cdot \sqrt{1+ {2\over \sqrt{5}}}} $$ sized radius should be calculated: https://en.wikipedia.org/wiki/Circle_packing_in_a_circle
I tried a lot to find some kind of literature article about this, but I couldn't find an obvious derivation for the radius in case $n=15$.
Finally, I tried to calculate the length of the radius myself, but it was beyond my abilities.