Phi - Wikipedia

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 functions in quantum mechanics, such as in the Schrödinger equation and bra–ket notation: ⟨ ϕ | ψ ⟩ {\displaystyle \langle \phi |\psi \rangle }  .
• The golden ratio 1 + 5 2 ≈ {\displaystyle {\tfrac {1+{\sqrt {5}}}{2}}\approx }   1.618033988749894848204586834... in mathematics,[3] art, and architecture. (Its reciprocal, 1/φ, is 5 − 1 2 {\displaystyle {\tfrac {{\sqrt {5}}-1}{2}}}   and is equal to φ − 1.)
• Euler's totient function φ(n) in number theory;[4] also called Euler's phi function.
• The cyclotomic polynomial functions Φn(x) of algebra.
• The number of electrical phases in a power system in electrical engineering, for example 1ϕ for single phase, 3ϕ for three phase.
• In algebra, group or ring homomorphisms
• In probability theory, φ ( x ) = ( 2 π ) − 1 2 e − x 2 2 {\textstyle \varphi (x)=(2\pi )^{-{\frac {1}{2}}}e^{-{\frac {x^{2}}{2}}}}   is the probability density function of the standard normal distribution.
• In probability theory, φX(t) = E[eitX] is the characteristic function of a random variable X.
• An angle, typically the second angle mentioned, after θ (theta).[5] It can denote:
  • The argument of a complex number.
  • The phase of a wave in signal processing.
  • In spherical coordinates, mathematicians usually refer to ϕ as the polar angle (from the z-axis). The convention in physics is to use ϕ as the azimuthal angle (from the x-axis).
  • One of the dihedral angles in the backbones of proteins 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 free energy destabilizations of protein mutants in phi value analysis.
• In combustion engineering, 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]
• 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, 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

In uppercase

The uppercase Φ is used as a symbol for:

• The cumulative distribution function (cdf) of standard normal distribution in statistics.
• The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
• Quantum yield, the number of times a specific event occurs per photon absorbed by a system.[6]
• In philosophy, Φ is often used as shorthand for a generic act. (Also in lowercase.)[citation needed]
• A common symbol for the parametrization of a surface in vector calculus.
• In Lacanian algebra, Φ stands for the imaginary phallus and also represents phallic signification; −Φ stands in for castration.[7][dubious – discuss]
• The diameter symbol in engineering, ⌀, is often erroneously referred to as "phi", and the diameter symbol is sometimes erroneously typeset as Φ. This symbol is used to indicate the diameter of a circular section; for example, "⌀14" means the diameter of the circle is 14 units.
• The null sign, ∅, which denotes the empty set in mathematics is sometimes also erroneously mistaken for phi.
• A clock signal in electronics is often called Phi or uses the symbol.[8]
• In emulsion and suspension science, Φ often denotes the volume fraction of the dispersed phase.[9]
• Archaically used in chemistry for phenyl group.
• Integrated information theory (IIT), a mathematical model for consciousness