1
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

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 $0.8804$.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.