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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

2 Answers 2

infinite, since the thickness cannot be computed because the fraction answer in infinite

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I suspect the question is asking for the case when all the circles are of equal radius, in which case it is always finite (but for arbitrarily small radius, arbitrarily many circles may fit) –  Meelo Dec 13 '14 at 19:12

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

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