In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich...

geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size...

Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It...

Random close packing (RCP) of spheres is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are...

the reals. Bin packing problem Close-packing of equal spheres Conway puzzle Covering problem Cutting stock problem Ellipsoid packing Kissing number problem...

this is called sphere packing, which usually deals only with identical spheres. The branch of mathematics generally known as "circle packing" is concerned...

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...

simultaneously square and triangular Close-packing of equal spheres Darling, David. "Cannonball Problem". The Internet Encyclopedia of Science. Ma, De Gong (1985)...

discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the close-packing of equal spheres the non-void fraction...

that "Proper use of Zen Magnets and Neoballs creates no exposure to danger whatsoever." As of January 2017, many brands of magnet spheres including Zen Magnets...

In geometry, sphere packing in a cube is a three-dimensional sphere packing problem with the objective of packing spheres inside a cube. It is the three-dimensional...

of packings that leave less empty space than is left by close-packing of equal spheres, and so many solids have been ruled out as counterexamples of Ulam's...

ISBN 052120125X. Boerdijk, A.H. (1952). "Some remarks concerning close-packing of equal spheres". Philips Res. Rep. 7: 303–313. Fuller, R.Buckminster (1975)...

mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater...

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

crystal structures of many metals can be described as a nearly mathematical close-packing of equal spheres. A simple model for both of these is to assume...

in each cell of the rhombic dodecahedral honeycomb, and it cannot be surpassed, since otherwise the optimal packing density of spheres could be surpassed...

including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys...

It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see Kepler...

sphere Homology sphere – Topological manifold whose homology coincides with that of a sphere Homotopy groups of spheres – How spheres of various dimensions...

unit sphere. For a given sphere packing (arrangement of spheres) in a given space, a kissing number can also be defined for each individual sphere as the...

is an integer The densest lattice packing of unit spheres in four dimensions (called the D4 lattice) places a sphere at every point whose coordinates are...

basis of geometry alone. While the problem of packing spheres of equal size has been well-studied since Gauss, Laves phases are the result of his investigations...

many theories of crystallography and solid state inorganic structure used collections of equal and unequal spheres to simulate packing and predict structure...

design from his work on close-packing of spheres. This involves connecting the sphere centers from cubic closest-packed spheres into a corresponding convex...

of a packing of equal spheres was still unsolved. The approach that Fejes Tóth suggested in that work, which translates as "packing [of objects] in a...

overlap. Lattice packings are special types of sphere packings where the spheres are centered at the points of a lattice. Placing spheres of radius 1/√2 at...

metamaterials Clock hypothesis Clockwork universe theory Close coupling Close-packing of equal spheres Closed system Closed timelike curve Closed wing Cloud...

configuration for the packing of four equal spheres. The dense random packing of hard spheres problem can thus be mapped on the tetrahedral packing problem. It...

arrangements of points on a sphere in various dimensions". Journal articles Tarnai T; Gáspár Zs (1987). "Multi-symmetric close packings of equal spheres on the...