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In mathematics, a ball is the space inside a sphere. It may be a closed ball (including the boundary points of the sphere) 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 dimensions is called an -ball and is bounded by an . 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 spherical shell boundary. In other contexts, such as in Euclidean geometry and informal use, ''sphere'' is sometimes used to mean ''ball''. ==Balls in Euclidean space== In Euclidean -space, an (open) -ball of radius and center is the set of all points of distance < from . A closed -ball of radius is the set of all points of distance ≤ away from . In Euclidean -space, every ball is the interior of a hypersphere (a hyperball), that is a bounded interval when = 1, the interior of a circle (a disk) when = 2, and the interior of a sphere when = 3. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ball (mathematics)」の詳細全文を読む スポンサード リンク
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