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 πR² (see π).

A ball is an extension of the concept of a disk to generalised metric spaces. Sometimes however, one uses the word "disk" synonymously with "ball", allowing a disk to have other dimensions.

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