Ball (mathematics)

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a ball is the <a href="/facts/Solid_geometry/tHH3JFoq">solid figure</a> bounded by a <a href="/facts/Sphere/jywYLNM2">sphere</a>; it is also called a solid sphere. It may be a closed ball (including the <a href="/facts/Boundary_points/WgdH18kp">boundary points</a> that constitute the sphere) or an open ball (excluding them).
These concepts are defined not only in three-dimensional <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a> but also for lower and higher dimensions, and for <a href="/facts/Metric_space/gnBBRXtc">metric spaces</a> in general. A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or <a href="/facts/N-sphere/bFu2S7E2">(n−1)-sphere</a>. Thus, for example, a ball in the <a href="/facts/Euclidean_plane/tAUtRFcn">Euclidean plane</a> is the same thing as a <a href="/facts/Disk_(mathematics)/DgMVr97H">disk</a>, the area bounded by a <a href="/facts/Circle/9fy5ggKn">circle</a>. In <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean 3-space</a>, a ball is taken to be the <a href="/facts/Volume/aeAXCBUd">volume</a> bounded by a <a href="/facts/2-sphere/jywYLNM2">2-dimensional sphere</a>. In a <a href="/facts/One-dimensional_space/bC4W2dHd">one-dimensional space</a>, a ball is a <a href="/facts/Line_segment/V8E0M4qk">line segment</a>.
In other contexts, such as in <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean geometry</a> and informal use, sphere is sometimes used to mean ball. In the field of <a href="/facts/Topology/2EqW47cU">topology</a> the closed 
 
 
 
 n
 
 
 {\displaystyle n}
 
-dimensional ball is often denoted as 
 
 
 
 
 B
 
 n
 
 
 
 
 {\displaystyle B^{n}}
 
 or 
 
 
 
 
 D
 
 n
 
 
 
 
 {\displaystyle D^{n}}
 
 while the open 
 
 
 
 n
 
 
 {\displaystyle n}
 
-dimensional ball is 
 
 
 
 int
 ⁡
 
 B
 
 n
 
 
 
 
 {\displaystyle \operatorname {int} B^{n}}
 
 or 
 
 
 
 int
 ⁡
 
 D
 
 n
 
 
 
 
 {\displaystyle \operatorname {int} D^{n}}
 
.

Ball (mathematics) open-in-new

Ball (mathematics)