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In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated packing density , η, of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called sphere packing , which usually deals only with identical spheres.
The branch of mathematics generally known as "circle packing" is concerned with the geometry and combinatorics of packings of arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping, Riemann surfaces and the like.
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