Hi,
How to calculate number of circles in side a square, if we know the side of the square and the circles all are equal size.
Thanks.
Hi, How to calculate number of circles in side a square, if we know the side of the square and the circles all are equal size. Thanks. 


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The right question is: given a positive integer $n$, what is the largest $r$ such that $n$ nonoverlapping circles of radius $r$ can fit inside a unit square? It's not simply a matter of hexagonal closepacking, because boundary effects are important. There is no known closedform formula, and not likely to be one, but the values are known for $n$ up to 30. See http://en.wikipedia.org/wiki/Circle_packing_in_a_square and http://hydra.nat.unimagdeburg.de/packing/csq/csq.html 


Given a square of side $L$, the area covered by circles, including partial circles, will be $\frac{\pi L^2}{\sqrt{12}}$; since the optimal circle packing density in the plane is $\frac{\pi}{\sqrt{12}}$. Therefore, given circles of radius $r$, the number of circles which fit in the square should be the greatest integer less than $\frac{1}{\sqrt{12}}\frac{L^2}{r^2}$ 

