Definition:Annulus (Geometry)

This page is about annulus in the context of geometry. For other uses, see annulus.

Definition

An annulus is a plane figure whose boundary consists of $2$ concentric circles:

In the above diagram, the annulus is the colored area.

Center of Annulus

The center of an annulus is the common center of the $2$ concentric circles that form its boundary.

In the above diagram, the center is the point $O$.

Inner Radius of Annulus

The inner radius of an annulus is the radius of the smaller of the $2$ concentric circles that form its boundary.

In the above diagram, the inner radius is denoted $r$.

Outer Radius of Annulus

The outer radius of an annulus is the radius of the larger of the $2$ concentric circles that form its boundary.

In the above diagram, the outer radius is denoted $R$.

Width of Annulus

The width of an annulus is the difference between its outer radius and the inner radius

In the above diagram, the width of the annulus is $R - r$.

Also known as

The more contemporary word ring can sometimes be seen for annulus.

However, as the term ring is ubiquitous in the field of abstract algebra to refer to an algebraic structure of a particular type, it is the policy of $\mathsf{Pr} \infty \mathsf{fWiki}$ to use the term annulus instead, so as to reduce the possibility of confusion.

Also see

• Results about annuli can be found here.

Linguistic Note

The word annulus (pronounced an-nu-lus) is Latin for little ring.

Its plural form is annuli (pronounced an-nu-lee).

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): annulus: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): annulus
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): annulus
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): annulus (annuli)

• Weisstein, Eric W. "Annulus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Annulus.html