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

Question

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

Simon Hayward · Answer 1 · 2012-12-17 14:57:27Z

up vote 0 down vote

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

edited Dec 17 '12 at 14:57

Simon Hayward
572513

answered Dec 17 '12 at 14:30

tappleman
1

	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 at 22:13

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