Definition:Disk

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Complex disk

Let $a \in \C$ be a complex number.

Let $R>0$ be a real number.

Open disk

The open (complex) disk of center $a$ and radius $R$ is the set:

$\map B {a, R} = \set {z \in \C: \cmod {z - a} < R}$

where $\cmod {\, \cdot \,}$ denotes complex modulus.

Closed disk

The closed (complex) disk of center $a$ and radius $R$ is the set:

$\map B {a, R} = \set {z \in \C: \cmod {z - a} \le R}$

where $\cmod {\, \cdot \,}$ denotes complex modulus.

Euclidean disk

Let $n \ge 1 $ be a natural number.

Let $\struct {\R^n, d}$ be the $n$-dimensional Euclidean space, where $d$ is the Euclidean metric.

Let $a \in \R^n$.

Let $r > 0$ be a real number.

Open disk

The open $n$-disk of center $a$ and radius $r$ is the set:

$\map {\mathbb D^n} {a, r} = \set {x \in \R^n: \map d {x, a} < r}$

Closed disk

A closed $n$-disk of center $a$ and radius $r$ is the set:

$\map {\overline {\mathbb D}^n} {a, r} = \set {x \in \R^n: \map d {x, a} \le r}$

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The boundary of $\mathbb D^n$ is denoted $\partial \mathbb D^n$, and is $\mathbb S^{n - 1}$, the $\paren {n - 1}$-sphere.

Radius of Disk

Let $\map B {a, r}$ be a disk.

The radius of $\map B {a, r}$ is the parameter $r$.

Center of Disk

Let $\map B {a, r}$ be a disk.

The center of $\map B {a, r}$ is the parameter $a$.

Also see

• Definition:Unit Disk
• Definition:Polydisk
• Definition:Ball
• Definition:Sphere
• Boundary of Disk is Sphere

• The open disc of radius $r$ is a particular instance of an open $r$-ball in $\struct {\R^n, d}$.

Internationalization

Disk is translated:

In Dutch:

schijf

(literally: disk)

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): disc
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): disk