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then the question is,the larger radius D,the small radius d,get the largest number of small circle put in the larger?

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See this and this. – J. M. Jan 5 '12 at 10:39
See also Circle packing in a circle. – lhf Jan 5 '12 at 15:09
I believe this is still an open problem. – Rogelio Molina Apr 24 '15 at 5:52

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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I made some edits to the typesetting. Please check that I've left the meaning the same. – Simon Hayward Dec 17 '12 at 14:53
I'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 $O(\frac{R}{r})$. – Steven Stadnicki May 3 '13 at 22:13

protected by Zev Chonoles Jul 12 at 3:13

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