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\geq 1 $ be a natural number.
Let $\left({\R^n, d}\right)$ 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:
- $\mathbb D^n(a, r) = \left\{{x \in \R^n : d \left({x, a}\right) < r}\right\}$
Closed disk
A closed $n$-disk of center $a$ and radius $r$ is the set:
- $\overline {\mathbb D}^n(a, r) = \left\{{x \in \R^n : d \left({x, a}\right) \le r }\right\}$
The boundary of $\mathbb D^n$ is denoted $\partial \mathbb D^n$, and is $\mathbb S^{n-1}$, the $(n-1)$-sphere.
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 $\left({\R^n, d}\right)$.
Internationalization
Disk is translated:
In Dutch: | schijf | (literally: disk) |