How do you pack circles into a circle? I want to know how many small circles can be packed into a large circle.
Looking at Erich's Packing Center it seems that packing is a non-trivial problem to solve.
My interest is practical rather than theoretical, so I don't really care about the absolute upper bound. I just want a good enough solution that doesn't waste too much empty space.
Also, I have a range of acceptable diameters for the small circles. So it's not necessarily a question of packing $x$ circles into $1$ circle, but packing $x, x+1, ... x+n$ circles into a circle, and seeing which one looks nicer. For instance, looking at EPC, $16$ and $18$ circles in one circle seems to be much prettier than $17$ - so even if I was looking for $17$ ideally, I would compromise by either using smaller circles or fewer circles instead.
So to solve my problem, I need a general, easily computable algorithm for packing $n$ circles into $1$ circle. I suspect this does not exist (otherwise EPC wouldn't). What about a general, easily computable algorithm that packs $n$ circles into a circle "well enough"?

Have you tried just packing them on the boundary? (I'll explain what I mean below). 
Let $C$ be the circle of radius $R$ and order your $N$ circles as $C_1,\cdots,C_N$ such that $r_1 \ge r_2 \ge \cdots \ge r_N$. Place $C_1$ inside $C$ tangent to $C$. Then place $C_2$ tangent to $C_1$ and $C$, $C_3$ tangent to $C_2$ and $C$, $C_4$ tangent to $C_3$ and $C$, and keep going until the circle tangent to $C_n$ and $C$ has to intersect $C_1$. Then just "keep going around" (letting $C_{n+1}$ be the unique circle of radius $r_{n+1}$ tangent to $C_1$ and $C_n$). 
Of course, this algorithm is not optimal and doesn't always work, but "it won't waste too much space" if it works. If you had values of $r_i$ and $R$ and the remaining space was too big, you can always retry with a smaller value of $R$.
Hope that helps,
