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...

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

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

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...

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'...

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...

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...

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...

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}...

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

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...

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

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...

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

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

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

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

\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...

the 'inspheres' of their polyhedra. Circumscribed sphere Inscribed circle Midsphere Sphere packing Coxeter, H.S.M. Regular Polytopes 3rd Edn. Dover (1973)...

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

However, sphere packing problems can be generalised to consider unequal spheres, n-dimensional Euclidean space (where the problem becomes circle packing in...

honeycombs, the tesseractic honeycomb corresponds to a sphere packing of edge-length-diameter spheres centered on each vertex, or (dually) inscribed in each...

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

Romik published a paper simplifying Maryna Viazovska's solution to the sphere packing problem in dimension 8. Viazovska's original solution relied on computer...

also lists the 18th problem as "open" in his 2000 book, because the sphere-packing problem (also known as the Kepler conjecture) was unsolved, but a solution...