Max Squares Fitting in a Circle: Proof & Formulas

[simpleton]

Hi,

Given that the radius of a circle is X, and the side length of a square is Y, what is the maximum number of squares you can fill inside this circle, provided that the squares do not overlap? If you know of a general formula or something, can you please tell me the proof or give me a link to the proof or something?

Thanks a lot.

 

[Gerenuk]

Have a look at
http://www2.stetson.edu/~efriedma/packing.html
http://en.wikipedia.org/wiki/Packing_problem
http://mathworld.wolfram.com/SquarePacking.html
which gives you the answer. Consider scaling to connect it to your problem with X and Y.

I haven't heard of a general formula. But with large circles one could write down an (ugly?) formula for the bounds to the number of squares by assuming gapless packing.

Maybe for very large circles the gapless packing is even optimal? Not sure about how much the boundaries matter.

 

[CRGreathouse]

Maybe for very large circles the gapless packing is even optimal? Not sure about how much the boundaries matter.

Probably "square root"-ly. So not much if you're concerned about the percentage filled, but a lot if you care about the amount not filled.