Annuliareas

Annuliareas is an informal term used to describe ring-shaped regions or zones bounded by two concentric curves, typically circles. The word combines annuli (plural of annulus, from Latin for "ring") and areas, and is applied across mathematics, physical sciences, and applied fields to denote regions that are annular in shape.

In elementary geometry an annulus is the planar region between two concentric circles of radii r and R (R > r); its area equals π(R^2 − r^2). In topology an annular region is often called an annulus and is homeomorphic to the product of a circle and a closed interval (S^1 × [0,1]), providing a simple example of a two-dimensional manifold with boundary.

Annuliareas or annular regions appear in diverse applications: in optics and imaging (radial filters or masking), in engineering (ring-shaped components and stress analysis), in ecology (habitat zones surrounding a point source), and in dendrochronology (analysis of growth rings when translated into spatial sectors). In data analysis and geospatial work, annular sampling is used to study radial patterns and gradients.

Although not a standard technical term in most disciplines, annuliareas serves as a convenient descriptive label for discussions of ring-shaped spatial patterns and measurements. Related concepts include annulus, concentric circles, radial symmetry, and ring topology.