In any dimension the sphere-packing problem is the question of how equal-size spheres can be arranged with as little empty space between them as possible. Whereas it would seem logical for ...

His statement that the closest packing gives an increase in density as the size of sphere is decreased appears to be derived from an incorrect conception of what constitutes the closest packing.

AT the present time when economy of material is so important, the problem of the open packing of spheres possesses ... in which each sphere makes contact with three others, and which shall be ...

In a pair of papers posted online this month, a Ukrainian mathematician has solved two high-dimensional versions of the centuries-old “sphere packing” problem. In dimensions eight and 24 (the latter ...

Mathematicians have long known that it’s possible to pack at most 12 identical spheres around and touching a 13th. Dodecahedron. In 1943, Hungarian mathematician L. Fejes Tóth conjectured that ...

Hanumantha Rao Vutukuri in the TNW Faculty, along with Utrecht University, have investigated this fascinating mathematical sphere-packing problem by combining experiments and computer simulations.

Such transmission of data can generate errors. Exploring sphere-packing in higher dimensions actually has implications for how we detect and correct those errors. But sphere-packing is a hard problem.

What is the most space-efficient way to pack tennis balls or oranges? Mathematicians have studied this “sphere-packing” problem for centuries, but surprisingly little attention has been paid ...