Symbols:Greek/Phi
Phi
The $21$st letter of the Greek alphabet.
- Minuscules: $\phi$ and $\varphi$
- Majuscules: $\Phi$ and $\varPhi$
The $\LaTeX$ code for \(\phi\) is \phi
.
The $\LaTeX$ code for \(\varphi\) is \varphi
.
The $\LaTeX$ code for \(\Phi\) is \Phi
.
The $\LaTeX$ code for \(\varPhi\) is \varPhi
.
Euler Phi Function
- $\map \phi n$
Let $n \in \Z_{>0}$, that is, a strictly positive integer.
The Euler $\phi$ (phi) function is the arithmetic function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:
- $\map \phi n = $ the number of strictly positive integers less than or equal to $n$ which are prime to $n$
That is:
- $\map \phi n = \card {S_n}: S_n = \set {k: 1 \le k \le n, k \perp n}$
The $\LaTeX$ code for \(\map \phi n\) is \map \phi n
.
Golden Mean
- $\phi$
Let a line segment $AB$ be divided at $C$ such that:
- $AB : AC = AC : BC$
Then the golden mean $\phi$ is defined as:
- $\phi := \dfrac {AB} {AC}$
Mapping
- $\map \phi x$
The Greek letter $\phi$, along with $\psi$ and $\chi$ and others, is often used to denote a general mapping.
In the context of abstract algebra, it often denotes a homomorphism.
The $\LaTeX$ code for \(\map \phi x\) is \map \phi x
.
Magnetic Flux
- $\phi$
The usual symbol used to denote magnetic flux is the Greek letter $\phi$ (phi).
Its $\LaTeX$ code is \phi
.
Longitude
- $\phi$
Used to denote the longitude of a given point in spherical coordinates.