# Ball (mathematics)

## Volume space bounded by a sphere / From Wikipedia, the free encyclopedia

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In mathematics, a **ball** is the solid figure bounded by a *sphere*; it is also called a **solid sphere**.^{[1]} It may be a **closed ball** (including the boundary points that constitute the sphere) or an **open ball** (excluding them).

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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 n dimensions is called a **hyperball** or **n-ball** and is bounded by a *hypersphere* or (*n*−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment.

In other contexts, such as in Euclidean geometry and informal use, *sphere* is sometimes used to mean *ball*. In the field of topology the closed $n$-dimensional ball is often denoted as $B^{n}$ or $D^{n}$ while the open $n$-dimensional ball is $\operatorname {Int} B^{n}$ or $\operatorname {Int} D^{n}$.