Cannonball in the context of Sphere packing


Cannonball in the context of Sphere packing

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⭐ Core Definition: Cannonball

A round shot (also called solid shot or simply ball) is a solid spherical projectile without explosive charge, launched from a gun. Its diameter is slightly less than the bore of the barrel from which it is shot. A round shot fired from a large-caliber gun is also called a cannonball.

The cast iron cannonball was introduced by French artillery engineers after 1450; it had the capacity to reduce traditional English castle wall fortifications to rubble. French armories would cast a tubular cannon body in a single piece, and cannonballs took the shape of a sphere initially made from stone material. Advances in gunpowder manufacturing soon led the replacement of stone cannonballs with cast iron ones.

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👉 Cannonball in the context of Sphere packing

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-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.

A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing 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.

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