2 research outputs found
Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio
We use computational experiments to find the rectangles of minimum area into
which a given number n of non-overlapping congruent circles can be packed. No
assumption is made on the shape of the rectangles. Most of the packings found
have the usual regular square or hexagonal pattern. However, for 1495 values of
n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,...
4999, we prove that the optimum cannot possibly be achieved by such regular
arrangements. The evidence suggests that the limiting height-to-width ratio of
rectangles containing an optimal hexagonal packing of circles tends to
2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure