A packing density or packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. In simplest...

space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending...

circle can be enlarged without creating an overlap. The associated packing density, η, of an arrangement is the proportion of the surface covered by the...

the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is π 3 2 ≈ 0.74048...

achieve a packing density greater than any smaller number > 1. (Higher density records all have rattles.) Disk covering problem Square packing in a circle...

find the configuration that packs a single container with the maximal packing density. More commonly, the aim is to pack all the objects into as few containers...

double lattice packing of the Euclidean plane of packing density approximately 0.89269. This has been conjectured to be the lowest density possible for...

otherwise the optimal packing density of spheres could be surpassed by putting a sphere in each rhombicuboctahedron of the hypothetical packing which surpasses...

monolayer (SAM) enable variations of desired probe packing density. The density of aptamer packing on the electrode surface is an important parameter...

is only one nontrivial packing density. Walter Stromquist (unpublished) settled this case by showing that the packing density of 132 is 2√3 − 3, approximately...

higher the packing density, the less empty space there is in the packing and thus the smaller the volume of the hull (in comparison to other packings with the...

close-packed density for this particular procedure of packing. The random close packing is the highest possible volume fraction out of all possible packing procedures...

three-dimensional equivalent of the circle packing in a circle problem in two dimensions. Best packing of m>1 equal spheres in a sphere setting a new density record...

disordered packing at densities exceeding 78%. For a periodic approximant to a quasicrystal with an 82-tetrahedron unit cell, they obtained a packing density as...

923,} which is the density of one possible double lattice packing for these shapes. The best proven upper bound on the packing density is approximately...

Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ρ (the...

Packing fraction may refer to: Packing density, the fraction of the space filled by objects comprising the packing Atomic packing factor, the fraction...

three-dimensional convex body with lower packing density than the sphere? More unsolved problems in mathematics Ulam's packing conjecture, named for Stanisław...

In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied...

any edge-to-edge tiling made by regular polygons: The maximum known packing density of a regular pentagon is ( 5 − 5 ) / 3 ≈ 0.921 {\displaystyle (5-{\sqrt...

This number is a measure of the local packing density around a given residue. The influence of local packing density can be assessed by series expansion...

nanoparticles. The methods differ by their ability to control particle packing density and layer thickness, ability to use different particles and the complexity...

eyes. AOSLO has also revealed significant decreases in foveal cone packing density for myopic eyes in comparison to emmetriopic eyes. This difference...

called asymptotic density) Dirichlet density Packing density Density (polytope) Density on a manifold Tensor density in differential geometry Dense set...

chemistry. Barium ferrite is a highly magnetic material, has a high packing density,[clarification needed] and is a metal oxide. Studies of this material...

sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than...

head size. Furthermore, bird brains have two-to-four times the neuron packing density of mammal brains, for higher overall efficiency. The visual and auditory...

Circle packing in a square is a packing problem in recreational mathematics where the aim is to pack n unit circles into the smallest possible square....

aneurysms by limiting blood circulation to the aneurysm space. Clinically, packing density is recommended to be 20-30% or more of the aneurysm's volume, typically...

Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder...