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| | '''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[1]</sup> and ˈfi in [[Modern Greek language|modern Greek]], is the 21st letter of the [[Greek alphabet]]. In modern Greek, it represents [f], a [[voiceless labiodental fricative]]. In Ancient Greek it represented [pʰ], an [[Aspiration (phonetics)|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)|ph]]" in words derived from Greek). In the system of [[Greek numerals]] it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter [[Ef (Cyrillic)|Ef]] (Ф, ф) arose from Φ. | | '''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[1]</sup> and ˈfi in [[Modern Greek language|modern Greek]], is the 21st letter of the [[Greek alphabet]]. In modern Greek, it represents [f], a [[voiceless labiodental fricative]]. In Ancient Greek it represented [pʰ], an [[Aspiration (phonetics)|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)|ph]]" in words derived from Greek). In the system of [[Greek numerals]] it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter [[Ef (Cyrillic)|Ef]] (Ф, ф) arose from Φ. |
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| - | == Use as a symbol ==
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| - | The lower-case letter <math>\varphi \,</math> (or often its variant, <math>\phi \,</math>) is often used to represent the following:
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| - | *The [[golden ratio]] <math>\tfrac{1 + \sqrt{5}}{2} \approx 1.61803\ldots</math> in mathematics, art, and architecture.
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| - | *[[Euler's totient function]] ''φ''(''n'') in number theory; also called ''Euler's phi function''.
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| - | *In algebra, [[Group (mathematics)|group]] or [[Ring (mathematics)|ring]] [[homomorphism]]s
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| - | * In [[probability theory]], {{nowrap|1=''ϕ''(''x'') = (2π)<sup>−½</sup>''e''<sup>−''x''<sup>2</sup>/2</sup>}} is the [[probability density function]] of the [[normal distribution]].
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| - | * In [[probability theory]], {{nowrap|1=''φ''<sub>''X''</sub>(''t'') = E[ ''e''<sup>''itX''</sup> ]}} is the [[characteristic function (probability theory)|characteristic function]] of a random variable ''X''.
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| - | *An [[angle]], typically the second angle mentioned, after ''θ'' ([[theta]]). Especially:
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| - | **The argument of a [[complex number]].
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| - | **The [[phase (waves)|phase of a wave]] in signal processing.
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| - | **In [[spherical coordinates]], mathematicians usually refer to phi as the polar angle (from the ''z''-[[Coordinate axis|axis]]). The convention in physics is to use phi as the azimuthal angle (from the ''x''-axis).
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| - | **One of the [[dihedral angle]]s in the backbones of [[protein]]s.
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| - | **Internal or effective [[angle of friction]].
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| - | *[[Electric potential]] in physics.
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| - | *The [[work function]] in electronics.
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| - | *A [[shorthand]] representation for an [[aromatic]] [[functional group]] in [[organic chemistry]].
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| - | *The [[fugacity]] coefficient in [[thermodynamics]].
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| - | *The ratio of [[Thermodynamic free energy|free energy]] destabilizations of protein [[mutant]]s in [[phi value analysis]].
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| - | *In [[cartography]] and [[navigation]], [[latitude]].
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| - | *In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
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| - | *A sentence in [[first-order logic]].
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| - | *[[Porosity]] in geology and [[hydrology]].
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| - | *Strength (or resistance) reduction factor in [[structural engineering]], used to account for statistical variabilities in materials and construction methods.
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| - | *The symbol for a [[voiceless bilabial fricative]] in the [[International Phonetic Alphabet]] (using the straight line variant character)
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| - | *In economics, this is usually an additive term.
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| - | *In [[flight dynamics]], the roll angle.
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| - | The upper-case letter Φ is used as a symbol for:
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| - | *The [[Golden_ratio#Golden_ratio_conjugate|golden ratio conjugate]] −0.618... in mathematics.
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| - | *The [[magnetic flux]] and [[electric flux]] in physics, with subscripts distinguishing the two.
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| - | *The [[cumulative distribution function]] of the [[normal distribution]] in [[mathematics]] and [[statistics]].
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| - | *[[Philosophy]].
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| - | *The number of phases in a power system in [[electrical engineering]], for example 1Φ for [[single phase]], 3Φ for [[three phase]].
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| - | *A common symbol for the parametrization of a surface in vector [[calculus]].
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| - | *In [[Lacanian algebra]], Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.<sup>[2]</sup>
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| - | The [[diameter]] symbol 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 [[circle]] is 14 [[Units of measurement|units]].
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| | == See also == | | == See also == |
