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Disk (mathematics)




In Geometry , a disk (also spelled '''disc''') is the region in a Plane contained inside of a Circle .

A disk is said to be ''closed'' or ''open'' according to whether it contains or not the circle which is its boundary. In Cartesian Coordinates , the open disk of center (a, b) and radius ''R'' is given by the formula
:D=\{(x, y)\in {\mathbb R^2}: (x-a)^2+(y-b)^2 < R^2\}
while the closed disk of the same center and radius is given by
:\overline{ D }=\{(x, y)\in {\mathbb R^2}: (x-a)^2+(y-b)^2 \le R^2\}.

The Area of a disk of radius ''R'' (whether open or closed) is π''R''2 (see π ).

A ''ball'' is a disk in a space with more than two dimensions. See Ball (mathematics) . Sometimes however, one uses the word "disk" Synonymously with "ball", allowing a disk to have other dimensions.


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