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Math Problem

  1. Oct 12, 2009 #1
    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.
     
  2. jcsd
  3. Oct 12, 2009 #2
    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.
     
  4. Oct 12, 2009 #3

    CRGreathouse

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    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.
     
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