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