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
- Apollonian sphere packing
- Close-packing of equal spheres
- Geometry
- Hermite constant
- Kissing number problem
- Pattern
- Random close pack
- Sphere
- Sphere-packing bound
External links
- Sphere packing @ Wikipedia
