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.
Read more about Ball (mathematics): Balls in General Metric Spaces, Balls in Normed Vector Spaces, Topological Balls
Famous quotes containing the word ball:
“I never knew anyone yet who got up at six who did anything more useful between that time and breakfast than banging a tennis ball up against the side of the house, waiting for the more civilized members of the party to get up.”
—Robert Benchley (1889–1945)