If we're packing circles, don't we need to take into account that the 6ft distance is to the next person -- that is the centre of the next circle, rather than t

If we're packing circles, don't we need to take into account that the 6ft distance is to the next person -- that is the centre of the next circle, rather than the boundary of it? That means circles of radius 3ft, for a total of 8,693 square miles.