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
Close-packing of equal spheres (fcc) (also called cubic close packed) and hexagonal close-packed (hcp), based on their symmetry. Both are based upon sheets of spheres arranged at the vertices of a triangular tiling; they differ in how the sheets are stacked upon one another. The fcc lattice is also known to mathematicians as that generated by the A root system. The problem of close-packing of spheres was first mathematically analyzed by Thomas Harriot around 1587, after a question on piling cannonballs on ships was posed to him by Sir Walter Raleigh on their expedition to America. Cannonballs were usually piled in a rectangular or