# disk (mathematics)

A disk in mathematics, roughly speaking, is the "filling" of a circle.
A flat (two-dimensional) disk of radius *r* consists of all the points
that are at a distance ≤ *r* (**closed disk**) or < *r* (**open
disk**) from a fixed point in the plane. More generally, an *n*-dimensional
disk of radius *r* is the set of all points at a distance ≤ *r* (**closed**) or < *r* (**open**)
from a fixed point in Euclidean *n*-space. A disk is the two-dimensional
analog of a ball.