Sphere packing

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a sphere packing is an arrangement of non-overlapping <a href="/facts/Sphere/jywYLNM2">spheres</a> within a containing space. The spheres considered are usually all of identical size, and the space is usually three-<a href="/facts/Dimension/0ktmUyac">dimensional</a> <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a>. However, sphere <a href="/facts/Packing_problem/nQtnMb6Y">packing problems</a> can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes <a href="/facts/Circle_packing/nKFWD2ug">circle packing</a> in two dimensions, or <a href="/facts/Hypersphere/bFu2S7E2">hypersphere</a> packing in higher dimensions) or to <a href="/facts/Non-Euclidean_geometry/efKa7De2">non-Euclidean</a> spaces such as <a href="/facts/Hyperbolic_space/kI7tnwdk">hyperbolic space</a>.
A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the <a href="/facts/Packing_density/NY81NF80">packing density</a> 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 <a href="/facts/Average/etawWjw4">average</a> or <a href="/facts/Asymptotic/nvLPuxKa">asymptotic</a> density, measured over a large enough volume.
For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 63.5%.

Sphere packing open-in-new

Sphere packing