Euclidean annulus - Knowlpedia

For a center $a\in\mathbb R^n$ and radii $0<r<R$ , the open annulus is

A(a;r,R)=\{x\in\mathbb R^n:r<|x-a|<R\}.

Replacing one or both inequalities by non-strict ones gives half-open or closed versions. In two dimensions this is a ring-shaped region; in higher dimensions “spherical shell” is also used.

Cylindrical and dyadic versions

A cylindrical annular region in $\mathbb R^3$ restricts $\sqrt{x^2+y^2}$ between two positive radii, possibly also restricting $z$ . It stays away from the coordinate axis. A dyadic annulus has outer radius twice its inner radius and is useful for sorting estimates by scale.