If I have a square and want to place four equally large circles within this square, how large can the maximum radius be (compared to the lenght of the side of the square)?
Just an answer would be ok, but answer and explanation would be better.
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6$\begingroup$ This sort of question works better on the sites mentioned in the FAQ. $\endgroup$– Andrew StaceyCommented May 9, 2010 at 20:23
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$\begingroup$ I agree with Andrew Stacey. Also, you need to use more precise language. If the four circles are allowed to be coincident (to lie on top of each other), then the maximum radius is half the length of the square's side. $\endgroup$– JRNCommented Jan 8, 2012 at 0:40
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2 Answers
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See the links below. The solutions have been show to be optimal up to 20 circles into a square.
http://mathworld.wolfram.com/CirclePacking.html
A fun site about all kinds of packing results is:
answered May 9, 2010 at 20:13
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$\begingroup$ Thank you very much. For 4 circles the answer turns out to be boringly simple, the diameter is just half the length of the side. I was expecting that there existed some hexagonal packing more optimal than this when I asked the questing. $\endgroup$– hlovdalCommented May 9, 2010 at 20:27
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Here are some additional formulas/numbers about circle distances: http://en.wikipedia.org/wiki/Circle_packing_in_a_square
