Pack five unit circles in the smallest regular hexagon possible.
The exact solution for the smallest possible side length of the hexagon is given by the largest real root of a fourth degree polynomial:
Where a,b,c,d,e are integers. Find them.
On the internet I found a drawing of the figure. The side length (root) is given as well, but not the polynomial nor its derivation. For me, this is a good place to start, but one might also fairly regard this as a spoiler:
Edited on November 25, 2018, 11:01 am