Circle packing in a square

Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square; or, equivalently, to arrange n points in a unit square aiming to get the greatest minimal separation, d_n, between points. To convert between these two formulations of the problem, the square side for unit circles will be L = 2 + 2 d n .

Solutions (not necessarily optimal) have been computed for every N≤10,000. Solutions up to N=20 are shown below.: