Phi (letter)

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Greek alphabet
[[Image:Greek alphabet {{{letter\|alpha-omega}}}.png\| 200px\|center]]
Α α Alpha	Β β Beta
Γ γ Gamma	Δ δ Delta
Ε ε Epsilon	Ζ ζ Zeta
Η η Eta	Θ θ Theta
Ι ι Iota	Κ κ Kappa
Λ λ Lambda	Μ μ Mu
Ν ν Nu	Ξ ξ Xi
Ο ο Omicron	Π π Pi
Ρ ρ Rho	Σ σ ς Sigma
Τ τ Tau	Υ υ Upsilon
Φ φ Phi	Χ χ Chi
Ψ ψ Psi	Ω ω Omega
obsolete letters
Image:Greek alphabet digamma2.png Digamma	Image:Greek alphabet san.png San
Image:Greek alphabet qoppa.png Qoppa	Image:Greek alphabet sampi.png Sampi
Image:Greek alphabet stigma.png Stigma	Image:Greek alphabet sho.png Sho

Phi (upper case Φ or <math>\Phi</math>; lower case φ, Template:Phisymbol, <math>\phi</math> or <math>\varphi</math>) is the 21st letter of the Greek alphabet. In modern Greek it is pronounced fee, but a common anglicized pronunciation is fie. In modern Greek, it represents [[[Template:IPA]]], a voiceless labiodental fricative. In Ancient Greek it represented [[[Template:IPA]]], an aspirated voiceless bilabial plosive. In the system of Greek numerals it has a value of 500.

The lower-case letter φ (or often its variant, Template:Phisymbol) is used as a symbol for:

The golden ratio 1.618... in mathematics, art, and architecture.
Euler's totient function in number theory. Also called Euler's phi function, φ(n)
The argument of a complex number in mathematics.
The value of a plane angle in physics and mathematics.
Electric potential in physics.
The work function in electronics.
The phase of a wave in signal processing.
In spherical coordinates phi is usually used to represent the angle to the z axis.

The upper-case letter Φ is used as a symbol for;

In engineering, the diameter symbol Image:Boundy diameter symbol.png is often referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example Image:Boundy diameter symbol.png14 means the diameter of the circle is 14 units.
In structural engineering, Φ is notation for a strength (or resistance) reduction factor, used to account for statistical variabilities in materials and construction methods.
The magnetic flux in physics.
The Cumulative Normal Distribution function in statistics.
It is also used as a symbol/icon for philosophy.