Sphere packing
In geometry, Sphere packing refers to a number of problems that try to arrange spheres in space. Very often, the spheres all have the same size, and the space used is usually three-dimensional Euclidean space. The problem is part of packing problems. When it is generalised, not all the spheres need to have the same size, and spaces can be n-dimensional Euclidean space, or hyperbolic space.
A typical sphere packing problem is to find an arrangement in which the spheres fill as large a proportion of the space as possible. The proportion of space filled by the spheres is called the density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.
Sphere Packing Media
Sphere packing finds practical application in the stacking of cannonballs.
Regular arrangement of equal spheres in a plane changing to an irregular arrangement of unequal spheres (bubbles).
HCP lattice (left) and the FCC lattice (right) are the two most common highest density arrangements.
Two ways to stack three planes made of spheres
A dense packing of spheres with a radius ratio of 0.64799 and a density of 0.74786
_(cropped).jpg)
