I have an unlimited large plane. I am trying to calculated how many circles with a certain diameter d can fit into any square of size SxS on the plane. I think this should be the maximum density. So the question is NOT "How many circles can I fit into square of size x?", as it does not matter if the circles overlap the boundaries of the square.
(The setting is: How do I calculate how many people that try to keep distance d between their cores (modelled as circles) can fit into an area of size 1: What is the maximum density?)
I have looked into circle packing but that seems to calculate slightly different things.
I think it's either
2 / sqrt(3 * d * d)
2 / (sqrt(3) * d * d).
Any help (even a search word for google!) would be appreciated!