Definition:Disk
Definition
A disk in the pure geometrical context is a circular region of the plane, which may or may not include its boundary.
Open Disk
An open disk is a disk which does not include its boundary.
Closed Disk
A closed disk is a disk which includes its boundary.
Radius of Disk
The radius of a disk is the radius of the circle that forms its boundary.
Center of Disk
The center of a disk is the center of the circle that forms its boundary.
Also defined as
Many sources define a disk in the context of a general metric space as the set of points within a given distance of a given point.
That is, with the definition that $\mathsf{Pr} \infty \mathsf{fWiki}$ uses for ball.
It needs to be appreciated that when the metric space in question is a Euclidean plane, the two definitions coincide.
In fact, when the metric space in question is the complex plane, the term complex disk is used to mean the ball with the given radious and center.
While all terms are indeed aspects of the same thing, to reduce ambiguity, $\mathsf{Pr} \infty \mathsf{fWiki}$ insists on rigorous consistency in the use of these terms as defined here.
Also known as
The spelling of the word disk in British English is disc.
Also see
- Results about disks can be found here.
Internationalization
Disk is translated:
| In Dutch: | schijf | (literally: disk) |
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): disc
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): disk