Random close pack crystal lattices have maximum densities equal to this upper limit. Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction can be given as: "the volume taken by number of particles in a given space of volume". In other words, packing fraction defines the packing density. It has been shown that the filling fraction increases with
Sphere packing Sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing 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. 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