Disk (mathematics)
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Image:CIRCLE 1.svg 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 <math>(a, b)</math> and radius R is given by the formula
- <math>D=\{(x, y)\in {\mathbb R^2}: (x-a)^2+(y-b)^2 < R^2\}</math>
while the closed disk of the same center and radius is given by
- <math>\overline{ D }=\{(x, y)\in {\mathbb R^2}: (x-a)^2+(y-b)^2 \le R^2\}.</math>
The area of a disk of radius R (whether open or closed) is πR2 (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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