# how many smaller circles(radius is equal) I can fit within a larger circle

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

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
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