Sphere packing

File:HCP Oranges.jpg
The stacking of oranges is a practical application of sphere packing.

In geometry, Sphere packing refers to a number of problems that try to arrange spheres in space. Very often, the spheres all have the same size, and the space used is usually three-dimensional Euclidean space. The problem is part of packing problems. When it is generalised, not all the spheres need to have the same size, and spaces can be n-dimensional Euclidean space, or hyperbolic space.

A typical sphere packing problem is to find an arrangement in which the spheres fill as large a proportion of the space as possible. The proportion of space filled by the spheres is called the density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.