# Definition:Annulus (Geometry)

## 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.

## 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**

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