View source for Sphere packing

In [[geometry]], a '''sphere packing''' is an arrangement of non-overlapping spheres within a containing space.

== Dimensional space ==

The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, n-dimensional Euclidean space (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.

== Typical sphere packing problem ==

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.

For equal spheres the densest packing uses approximately 74% of the volume. Random packing of equal spheres generally have a density around 64%.

== See also ==

* [[Geometry]]
* [[Pattern]]
* [[Sphere]]

== External links ==

* [https://en.wikipedia.org/wiki/Sphere_packing Sphere packing] @ Wikipedia