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...

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

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...

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

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 Gang (1984)...

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

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...

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

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)...

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...

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...

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

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...

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...

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...

Journal articles Tarnai T; Gáspár Zs (1987). "Multi-symmetric close packings of equal spheres on the spherical surface". Acta Crystallographica. A43 (5):...

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

number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement...

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...

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...

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...

inscribed or circumscribed spheres, eventually solved using a method based on circle packing realizations, goes back to unpublished work of René Descartes circa...

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

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...

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

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...

ways of visualizing them. The principles involved can be understood by considering the most efficient way of packing together equal-sized spheres and stacking...