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

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

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...

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...

finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely...

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...

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

structures offer the best lattice packing of spheres, and is believed to be the optimal of all packings. With 'simple' sphere packings in three dimensions ('simple'...

Apollonian sphere packing is the three-dimensional equivalent of the Apollonian gasket. The principle of construction is very similar: with any four spheres that...

block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into...

n-dimensional spheres of a fixed radius in Rn so that no two spheres overlap. Lattice packings are special types of sphere packings where the spheres are centered...

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

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

2 December 1984) is a Ukrainian mathematician known for her work in sphere packing. She is a full professor and Chair of Number Theory at the Institute...

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

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

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...

spheres therefore must not intersect, we are faced with the problem of sphere packing. How many distinct codewords can we pack into our n {\displaystyle n}...

investigations. Square packing in a circle Circle packing in a circle Sphere packing in a cube Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1991)...

Sphere Packings, Lattices and Groups is a book about geometry and group theory by John Conway and Neil Sloane, with contributions by other mathematicians...

Sphere Napkin ring problem Orb (optics) Pseudosphere Riemann sphere Solid angle Sphere packing Spherical coordinates Spherical cow Spherical helix, tangent...

David Hilbert. It asks three separate questions about lattices and sphere packing in Euclidean space. The first part of the problem asks whether there...

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

projective line ⁠ O P 1 {\displaystyle \mathbf {OP} ^{1}} ⁠. 23-sphere A highly dense sphere-packing is possible in ⁠ 24 {\displaystyle 24} ⁠-dimensional space...

on the density of sphere packings using the Poisson summation formula, which subsequently led to a proof of optimal sphere packings in dimension 8 and...

contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the creator and maintainer of the On-Line...

also the odd Leech lattice), in 1940. Sphere packing E8 lattice Conway, J.H.; Sloane, N.J.A. (1999), Sphere packings, lattices and groups, Grundlehren der...

contact graph of a sphere packing (a graph where vertices are the centers of spheres and edges exist if the corresponding packing elements touch each...

\right)\right)+o\left(1\right)} Block codes are tied to the sphere packing problem which has received some attention over the years. In two dimensions...

defines the translative packing constant of that body. Atomic packing factor Sphere packing List of shapes with known packing constant Groemer, H. (1986)...