Let a circle $A$ which radius is $10 m$ and another circle is $B$ which radius is $0.2 m$.Is it possible to say that what is the maximum number of circles $B$ can be drawn in circle $A$?

I tried much but failed to calculate the area among four circles.Is there any general way to solve this type of problem.Please help me.


This is a well known problem related to the classical issue of packing circles. For packing equal unit circles in a larger circle with radius $R$, there are no "exact" closed formulas giving the maximal number of packable circles. It is known that the maximal density can be obtained using a hexagonal packing pattern, which for $R \rightarrow \infty$ provides an asymptotic density of $\pi \sqrt{3}/6\approx 0.9069$. Also, various maximal packing numbers have been demonstrated for trivial cases with $n$ small.

Googling on this topic you can find much other information. In your specific example, $R=50$: according to published tables, the maximal number of packable unit circles to date is believed to be $2201$, corresponding to a density of $0.8804$.

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