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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
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See also Circle packing in a circle. –  lhf Jan 5 '12 at 15:09

1 Answer 1

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
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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

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