In geometry, a disk (also spelt 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 <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.
See also
- Unit disk, a disk with radius one
- annulus (mathematics)
- Disk algebra
- Moment of inertia of a uniform disc
