I've just came back from my Mathematics of Packing and Shipping lecture, and I've run into a problem I've been trying to figure out.
Let's say I have a rectangle of length $l$ and width $w$.
Is there a simple equation that can be used to show me how many circles of radius $r$ can be packed into the rectangle, in the optimal way? So that no circles overlap. ($r$ is less than both $l$ and $w$)
I'm rather in the dark as to what the optimum method of packing circles together in the least amount of space is, for a given shape.
An equation with a non-integer output is useful to me as long as the truncated (rounded down) value is the true answer.
(I'm not that interested in how the circles would be packed, as I am going to go into business and only want to know how much I can demand from the packers I hire to pack my product)