# Minimum number of circles to fill up a square

Suppose there is a square each of side $a$. I want to fill the square with circle of radius $r$. How many overlapping circles are needed to fill up the square?

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exactly filling it up is not possible i guess, it becomes a quite tedious calculation ain't it? –  Bhargav Dec 27 '11 at 16:50
anyway related to this - stackoverflow.com/questions/7946152/… ? –  Bhargav Dec 27 '11 at 16:53
There probably is no "nice" exact formula for arbitrary a and r, but an overlapping hexagonal cover will be asymptotically optimal. –  Lopsy Dec 27 '11 at 18:10
Thank you very much for answers. –  user12290 Jan 2 '12 at 6:47