annuli

An annulus (plural annuli) is a ring-shaped region or structure bounded by two concentric circles. In geometry, it consists of all points whose distance from a fixed center lies between two radii, r and R, with 0 < r < R. The area is π(R^2 − r^2). An annulus may be described as open if the boundary circles are not included (r < distance < R) or closed if the boundaries are included (r ≤ distance ≤ R).

In complex analysis, an open annulus refers to the set {z ∈ C : r < |z| < R}. In practical terms, annuli arise when a region in the plane excludes a central disk.

Annuli appear in biology as ring-like structures. In ferns, the annulus is a ring of dead cells around a sporangium that helps release spores when moisture changes. In mycology, the term describes a ring on the stalk of a mushroom, left by the veil during development.

In anatomy, the annulus fibrosus is the tough outer ring of an intervertebral disc. In astronomy, annulus describes a ring-shaped region; during an annular solar eclipse, the Moon covers the center of the Sun, leaving a bright ring around it.

In optics, annular apertures or beams produce donut-shaped light patterns. The term broadly conveys a circular band with a hollow center, found across mathematics, science, and engineering.