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 all circles touch another. 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.

While the circle has a relatively low maximum packing density of 0.9069 on the Euclidean plane, it does not have the lowest possible. The "worst" shape to pack onto a plane is not known, but the smoothed octagon has a packing density of about 0.902414, which is the lowest maximum packing density known of any centrally-symmetric convex shape. Packing densities of concave shapes such as star polygons can be arbitrarily small.

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.

Read more about Circle Packing: Packings in The Plane, Packings On The Sphere, Packings in Bounded Areas, Unequal Circles

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... of allocations is referred to as the '

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... One such extension is to find the maximum possible density of a system with two specific sizes of

**circle**(a binary system) ... particular radius ratios permit compact

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...

**Circle packing**theorem For every connected simple planar graph G there is a

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### Famous quotes containing the words packing and/or circle:

“The good husband finds method as efficient in the *packing* of fire-wood in a shed, or in the harvesting of fruits in the cellar, as in Peninsular campaigns or the files of the Department of State.”

—Ralph Waldo Emerson (1803–1882)

“Sense is a line, the mind is a *circle*. Sense is like a line which is the flux of a point running out from itself, but intellect like a *circle* that keeps within itself.”

—Ralph J. Cudworth (1617–1688)