Ball (mathematics)

Ball (mathematics)

In mathematics, a ball is the space inside a sphere. It may be a closed ball (including the boundary points) or an open ball (excluding them).

These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball in the Euclidean plane, for example, is the same thing as a disk, the area bounded by a circle.

In mathematical contexts where ball is used, a sphere is usually assumed to be the boundary points only (namely, a spherical surface in three-dimensional space). In other contexts, such as in Euclidean geometry and informal use, sphere sometimes means ball.