Disk (mathematics)

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A disk is the inside of a circle.

In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle.

A disk is said to be closed or open according to whether or not it contains the circle that constitutes 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 closed or open disk of radius R is πR² (see π).

The ball is the disk generalised to metric spaces. However, sometimes "disk" is used to mean "ball".

In theoretical physics a disk is a rigid body which is capable of participating in collisions in a two-dimensional gas. Usually the disk is considered rigid so that collisions are deemed elastic.