- Phi (letter)
**Phi**(uppercase**Φ**, lowercase**φ**or**Unicode|ϕ**), pronounced [IPA|fī] in modern Greek and as [IPA|faɪ] in English, is the 21st letter of theGreek alphabet . In modern Greek, it represents [IPA|f] , avoiceless labiodental fricative . In Ancient Greek it represented [IPA|pʰ] , an aspiratedvoiceless bilabial plosive (from which English ultimately inherits the spelling "ph" in words derived from Greek). In the system ofGreek numerals it has a value of 500 (φʹ) or 500,000 (͵φ).The lower-case letter $varphi\; ,$ (or often its variant, $phi\; ,$) is used as a symbol for:

*Thegolden ratio 1.618... in mathematics, art, and architecture.

*Euler's totient function φ(n) in number theory; also called "Euler's phi function".

*Theprobability density function of thenormal distribution inmathematics andstatistics .

*Anangle , typically the second angle mentioned, after "θ" (theta ). Especially:

**The argument of acomplex number .

**The phase of a wave in signal processing.

**Inspherical coordinates , mathematicians usually refer to phi as the polar angle (from the "z"-axis). The convention in physics is to use phi as the azimuthal angle (from the "x"-axis).

**One of thedihedral angle s in the backbones ofprotein s.

**Internal or effectiveangle of friction

*Electric potential in physics.

*Thework function in electronics.

*Ashorthand representation for anaromatic functional group inorganic chemistry

*Thefugacity coefficient inthermodynamics

*The ratio of free energy destabilizations of proteinmutant s inphi value analysis

*Incartography andnavigation ,latitude .

*A sentence infirst-order logic .

*Porosity in geology.The upper-case letter Φ is used as a symbol for:

*The golden ratio conjugate 0.618... in mathematics.

*Themagnetic flux andelectric flux in physics, with subscripts distinguishing the two.

*Thecumulative distribution function of thenormal distribution inmathematics andstatistics .

*Philosophy .

*Strength (or resistance) reduction factor instructural engineering , used to account for statistical variabilities in materials and construction methods.

*The number of phases in a power system inelectrical engineering , for example 1Φ forsingle phase , 3Φ forthree phase .

*The symbol of thevoiceless bilabial fricative in theinternational phonetic alphabet .Thediameter symbol inengineering ,⌀ , is often incorrectly referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example ⌀14 means the diameter of thecircle is 14 units.**Computing**In

Unicode , there are multiple forms of the phi letter:

* upper case:

** U+03A6 GREEK CAPITAL LETTER PHI (Φ): Greek capital letter phi

* lower case:

** U+|03C6 GREEK SMALL LETTER PHI (φ): "letter" phi, used in Greek texts.

** U+03D5 GREEK PHI SYMBOL (Unicode|ϕ): phi "symbol", for mathematical and technical contexts. [*[*]*http://unicode.org/reports/tr25/#_Toc231 UTR #25: Unicode and Mathematics — Representative Glyphs for Greek Phi*]In HTML/

XHTML , the upper and lower case phicharacter entity reference s are`&Phi;`(Φ) and`&phi;`(φ) respectively.In

LaTeX , the math symbols are`Phi`($Phi,!$),`phi`($phi\; ,!$), and`varphi`($varphi,!$).In some browsers (e.g.

Internet Explorer 6 ), the shapes of the U+03C6 GREEK SMALL LETTER PHI (which should be viewed as a curl) and U+03D5 GREEK PHI SYMBOL (which should be viewed as a circle crossed by a slash) are exchanged. Compare these samples to check your browser::Phi letter: right $varphi,!$; possible wrong Unicode|φ

:Phi symbol: right $phi,!$; possible wrong Unicode|ϕ**ee also***F, f - Ef (Latin)

*Ф, ф - Ef (Cyrillic)**References**

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2010.*