Editing Phi (section)

=== In lowercase ===
The lowercase letter φ (or its variant, ϕ or ɸ) is often used to represent the following:
* The letter phi is commonly used in [[physics]] to represent [[wave function]]s in [[quantum mechanics]], such as in the [[Schrödinger equation]] and [[bra–ket notation]]: <math>\langle\phi|\psi\rangle</math>.
* The [[golden ratio]] <math>\tfrac{1 + \sqrt{5}}{2} \approx</math>  {{val|1.618033988749894848204586834}}... in mathematics,<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Golden Ratio|url=https://mathworld.wolfram.com/GoldenRatio.html|access-date=2020-08-10|website=mathworld.wolfram.com|language=en}}</ref> art, and architecture. (Its reciprocal, 1/φ, is <math>\tfrac{ \sqrt{5} - 1}{2}</math> and is equal to φ − 1.)
* [[Euler's totient function]] ''φ''(''n'') in number theory;<ref>{{Cite web|title=Euler's Totient Function {{!}} Brilliant Math & Science Wiki|url=https://brilliant.org/wiki/eulers-totient-function/|access-date=2020-08-10|website=brilliant.org|language=en-us}}</ref> also called ''Euler's phi function''.
* The [[cyclotomic polynomial]] functions Φ<sub>''n''</sub>(''x'') of algebra.
* The number of [[electrical phase]]s in a power system in [[electrical engineering]], for example 1ϕ for [[single phase]], 3ϕ for [[three phase]].
* In algebra, [[group (mathematics)|group]] or [[ring (mathematics)|ring]] [[homomorphism]]s
* In [[probability theory]],  <math display="inline">\varphi(x)=(2\pi)^{-\frac{1}{2}}e^{-\frac{x^2}{2}}</math> is the [[probability density function]] of the [[standard normal distribution]].
* 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''.
* An [[angle]], typically the second angle mentioned, after ''θ'' ([[theta]]).<ref>{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook|quote='''ϴ''','''φ''',ϴ,φ angle, angular displacement, angular separation, rotation angle |url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}</ref> It can denote:
** The argument of a [[complex number]].
** The [[phase (waves)|phase of a wave]] in signal processing.
** In [[spherical coordinates]], mathematicians usually refer to ϕ as the polar angle (from the ''z''-[[Coordinate axis|axis]]). The convention in physics is to use ϕ as the azimuthal angle (from the ''x''-axis).
** One of the [[dihedral angle]]s in the backbones of [[protein]]s in a [[Ramachandran plot]]
** Internal or effective [[angle of friction]].
** In [[cartography]] and [[navigation]], ɸ denotes [[latitude]]; likewise, in [[geodesy]] it denotes [[geodetic latitude]].
** In [[ship stability]], ɸ represents the [[angle of list]].
** In [[aircraft flight mechanics]] as the symbol for [[bank angle]] (sometimes represented with the letter theta, which is also used for pitch angle).
* The [[work function]] of a surface, in [[solid-state physics]].
* A [[shorthand]] representation for an [[aromatic]] [[functional group]] in [[organic chemistry]].
* The [[fugacity]] coefficient in [[thermodynamics]].
* The ratio of [[Thermodynamic free energy|free energy]] destabilizations of protein [[mutant]]s in [[phi value analysis]].
* In combustion engineering, [[Air–fuel ratio#Fuel–air equivalence ratio (ϕ)|fuel–air equivalence ratio]]. The ratio between the actual fuel-air ratio to the stoichiometric fuel-air ratio.
* In granulometry, [[sedimentology]], and [[soil engineering]], φ is a logarithmic unit of sediment [[grain size]], defined such that a change of 1 φ in grain size corresponds to a factor of 2 in grain diameter.
* A sentence in [[first-order logic]].
* The [[Veblen function]] in [[set theory]].
* [[Porosity]] in geology and [[hydrology]].
* Strength (or resistance) reduction factor in [[structural engineering]], used to account for statistical variabilities in materials and construction methods.
* The symbol for a [[voiceless bilabial fricative]] in the [[International Phonetic Alphabet]] (using the form ɸ).
* In [[philosophy]], φ is often used as shorthand for a [[generic act]]. (Also in uppercase.){{Citation needed|date=August 2018}}
* In [[perceptual psychology]], the [[phi phenomenon]] is the apparent motion caused by the successive viewing of stationary objects, such as the frames of a motion picture.
* In linguistics, [[Phi_features|φ-features]] denote features such as case, number and gender in which adjectives and pronouns agree with nouns.
* In [[lexical-functional grammar]], the function that maps elements from the [[c-structure]] to the [[f-structure]].
* In [[ecology]], [[site survival probability]], or the probability that a species will continue to occupy a site if it was there the previous year.
* The logo of [[La France Insoumise]], a leftist French [[political party]].
* An abbreviation for the word [[bacteriophage]]
** Mϕ is used as an abbreviation for the word [[macrophage]]