then the question is,the larger radius D,the small radius d,get the largest number of small circle put in the larger?
how many smaller circles(radius is equal) I can fit within a larger circle
6
$\begingroup$
geometry
packing-problem
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5See [this](http://www.jstor.org/pss/2688509) and [this](http://www2.stetson.edu/~efriedma/cirincir/). – 2012-01-05
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2See also [Circle packing in a circle](http://en.wikipedia.org/wiki/Circle_packing_in_a_circle). – 2012-01-05
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1I believe this is still an open problem. – 2015-04-24
1 Answers
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The answer can be closely approximated by this equation:
Number of Circles $= 0.83\frac{R_2^2}{r_1^2} - 1.9$ (rounded down to whole number)
where: $R_2$ = radius of larger circle $r_1$ = radius of smaller circle
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0I made some edits to the typesetting. Please check that I've left the meaning the same. – 2012-12-17
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4I'm skeptical of the result particularly for $R\gg r$; at that point you should be able to get arbitrarily close to the $\pi/\sqrt{12}\approx 0.9$ density of the full planar packing, minus some boundary effects that can't be any larger than $O(\frac{R}{r})$. – 2013-05-03