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
Square packing in a square 7, 8, 10, 14, 15, 24, and 35. The table below shows the optimal value of "a" for , with some example packings. Other results that do not establish exact optimal packings are known. For example: Square packing in a square Square packing in a square is a packing problem where the objective is to determine how many squares of side 1 (unit squares) can be packed into a square of side "a". If "a" is an integer, the answer is "a", but the precise, or even asymptotic, amount of wasted space for non-integer "a" is an open question. The