# Optimal size of n circles to fit an area

Let us say that I have a rectangular area that has to always look "filled" with circles. (the void spaces with the given number of circles should be minimal)(Goal)

Let us assume that, I am also told that there will be n circles that I want to fit into the container and I am also given relative sizes of different circles (i.e say that n/2 circles have to be twice the size of the remaining n/2 circles). Now the question is whether there is a way to synthesize the size of the circles such that te container looks "filled".

• Appolonian gaskets (en.wikipedia.org/wiki/Apollonian_gasket) spring to mind... – Johannes Jan 20 '15 at 13:25
• I think this is more a general math problem for mathsSE than a puzzle, unless you specify a very distinct problem to which a nice solution exists. I have voted for closure as off-topic asking to relocate the question. This is not meant as a turn-down, though. – BmyGuest Jan 22 '15 at 10:37
• The optimal size and packing will depend on r, the aspect ratio of the rectangle. Might as well pick, for illustration here, r = 2.0 – smci Feb 13 '18 at 9:42

• Stupid but probably good approximation: $n$ small circles fall into the container. Shake the container. Simulate physics. Grow the circles until they won't grow any more. – Lopsy Jan 21 '15 at 13:51