Disk (mathematics)

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In geometry, a disk (also spelled disc) is the region in a plane contained 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 <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 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.