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

Sphere packing is the problem of arranging non-overlapping spheres within some space, with the goal of maximizing the combined volume of the spheres.

Define the packing density of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for identical spheres: cubic …

I.e., to use space e ciently, want to maximize the packing density. Rapid, error-free communication requires a dense sphere packing. Real-world channels correspond to high …

Jul 7, 2025 · The sphere-packing problem — which asks how to cram balls into a (high-dimensional) box as efficiently as possible — is no exception. It has enticed mathematicians …

Nov 13, 2018 · Higher-dimensional sphere packings are important in communications technology, where they ensure that the messages we send via the internet, a satellite, or a telephone can …

In a periodic packing, spheres are not restricted to just the corners of a fundamental cell. No reason to believe densest packing must be periodic, but periodic packings come arbitrarily …

A packing inRnis a set of balls of the same radius, whose interiors are non-overlapping. For historical reasons, those packings are called sphere packings, instead of ball packings.

May 26, 1999 · The problem of finding the densest packing of spheres (not necessarily periodic) is therefore known as the Kepler Problem. The Kepler Conjecture is intuitively obvious, but the …

May 5, 2025 · The sphere packing problem in n -dimensional Euclidean space ℝ n asks for an arrangement of non-overlapping congruent spheres that fills the largest possible fraction of …