How many squares can be packed into a circle?

Question

How many squares of size a×a can be packed into a circle of radius R?

I don\'t need a solution. I just need some kind of a starting idea.

Answer 1

Just a shot in the dark after a few minutes of thought...

What if you worked with half the circle and doubled it at the end. I would start with a grid of squares the length of the diameter and the width of the radius, essentially blanketing the semi-circle. Then check all 4 corners of each square and make sure their coordinates are within the radius of the circle. This would of course require that you plot the circle and squares on some sort of coordinate system or grid.

I hope this makes sense... It's in my head and it seems a bit difficult to articulate :)

EDIT: After drawing it out, I think this method would work with a little tweaking. I would line up the squares along the diameter, but slide the first one down until it fits. Set that one in place and start lining up squares next to it until they no longer fit. Move out to the edge of this line of squares and repeat the same steps until your rows of squares reach the radius.