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
Circle packing in an equilateral triangle removing any single circle from the optimal hexagonal packing of circles. This conjecture is now known to be true for . Minimum solutions for the side length of the triangle: A closely related problem is to cover the equilateral triangle with a fixed number of equal circles, having as small a radius as possible. Circle packing in an equilateral triangle Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack "n" unit circles into the smallest possible equilateral triangle. Optimal solutions are known for "n" < 13 and for any triangular