- 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 the
Greek alphabet. In modern Greek, it represents [IPA|f] , a voiceless labiodental fricative. In Ancient Greek it represented [IPA|pʰ] , an aspirated voiceless bilabial plosive(from which English ultimately inherits the spelling "ph" in words derived from Greek). In the system of Greek numeralsit has a value of 500 (φʹ) or 500,000 (͵φ).
The lower-case letter (or often its variant, ) is used as a symbol for:
golden ratio1.618... in mathematics, art, and architecture.
Euler's totient functionφ(n) in number theory; also called "Euler's phi function".
probability density functionof the normal distributionin mathematicsand statistics.
angle, typically the second angle mentioned, after "θ" ( theta). Especially:
**The argument of a
**The phase of a wave in signal processing.
spherical 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 the
dihedral angles in the backbones of proteins.
**Internal or effective
angle of friction
Electric potentialin physics.
work functionin electronics.
shorthandrepresentation for an aromatic functional groupin organic chemistry
fugacitycoefficient in thermodynamics
*The ratio of free energy destabilizations of protein
mutants in phi value analysis
cartographyand navigation, latitude.
*A sentence in
The upper-case letter Φ is used as a symbol for:
*The golden ratio conjugate 0.618... in mathematics.
magnetic fluxand electric fluxin physics, with subscripts distinguishing the two.
cumulative distribution functionof the normal distributionin mathematicsand statistics.
*Strength (or resistance) reduction factor in
structural engineering, used to account for statistical variabilities in materials and construction methods.
*The number of phases in a power system in
electrical engineering, for example 1Φ for single phase, 3Φ for three phase.
*The symbol of the
voiceless bilabial fricativein the international phonetic alphabet.The diametersymbol in engineering, ⌀, 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 the circleis 14 units.
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] ]
XHTML, the upper and lower case phi character entity references are &Phi; (Φ) and &phi; (φ) respectively.
LaTeX, the math symbols are Phi (), phi (), and 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 ; possible wrong Unicode|φ
:Phi symbol: right ; possible wrong Unicode|ϕ
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