Difference between revisions of "Sphere packing"

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== See also ==
 
== See also ==
  
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* [[Apollonian sphere packing]]
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* [[Close-packing of equal spheres]]
 
* [[Geometry]]
 
* [[Geometry]]
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* [[Hermite constant]]
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* [[Kissing number problem]]
 
* [[Pattern]]
 
* [[Pattern]]
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* [[Random close pack]]
 
* [[Sphere]]
 
* [[Sphere]]
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* [[Sphere-packing bound]]
  
 
== External links ==
 
== External links ==

Latest revision as of 17:10, 24 May 2016

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

External links