Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ;
Modern Greek: ''fi'' ) is the 21st letter of the
Greek alphabet.
In
Archaic
Archaic is a period of time preceding a designated classical period, or something from an older period of time that is also not found or used currently:
*List of archaeological periods
**Archaic Sumerian language, spoken between 31st - 26th cent ...
and
Classical Greek (c. 9th century BC to 4th century BC), it represented an
aspirated voiceless bilabial plosive (), which was the origin of its
usual romanization as . During the later part of
Classical Antiquity, in
Koine Greek (c. 4th century BC to 4th century AD), its pronunciation shifted to that of a
voiceless bilabial fricative (), and by the
Byzantine Greek
Medieval Greek (also known as Middle Greek, Byzantine Greek, or Romaic) is the stage of the Greek language between the end of classical antiquity in the 5th–6th centuries and the end of the Middle Ages, conventionally dated to the Ottoman co ...
period (c. 4th century AD to 15th century AD) it developed its modern pronunciation as a
voiceless labiodental fricative
The voiceless labiodental fricative is a type of consonantal sound used in a number of spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is .
Some scholars also posit the voiceless labiodental approx ...
().
The
romanization of the Modern Greek phoneme is therefore usually .
It may be that phi originated as the letter
qoppa (Ϙ, ϙ), and initially represented the sound before shifting to Classical Greek . In traditional
Greek numerals, phi has a value of 500 () or 500,000 (). The Cyrillic letter
Ef (Ф, ф) descends from phi.
As with other Greek letters, lowercase phi (encoded as the
Unicode character ) is used as a mathematical or scientific symbol. Some uses, such as the
golden ratio, require the old-fashioned 'closed' glyph, which is separately encoded as the Unicode character .
Use as a symbol
The lowercase letter φ (or often its variant, ϕ) is often used to represent the following:
*
Magnetic flux
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ( ...
in
physics
* 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
In quantum mechanics, bra–ket notation, or Dirac notation, is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets".
A ket is of the form , v \rangle. Mathema ...
:
.
* The
golden ratio ... in mathematics, art, and architecture.
*
Euler's totient function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...
''φ''(''n'') in number theory; also called ''Euler's phi function''.
* The
cyclotomic polynomial
In mathematics, the ''n''th cyclotomic polynomial, for any positive integer ''n'', is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any Its roots are all ''n''th primiti ...
functions Φ
''n''(''x'') of algebra.
* The number of phases in a power system in
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, for example 1ϕ for
single phase, 3ϕ for
three phase.
* In algebra,
group or
ring
Ring may refer to:
* Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry
* To make a sound with a bell, and the sound made by a bell
:(hence) to initiate a telephone connection
Arts, entertainment and media Film and ...
homomorphisms
* In
probability theory, is the
probability density function of the
standard normal distribution.
* In
probability theory, is the
characteristic function of a random variable ''X''.
* An
angle, typically the second angle mentioned, after ''θ'' (
theta). It can denote:
** The argument of a
complex number.
** The
phase of a wave in signal processing.
** In
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 in a
Ramachandran plot
** Internal or effective
angle of friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of ...
.
* The
work function of a surface, in
solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the l ...
.
* 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
cartography,
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
and
navigation,
latitude.
* In
aircraft flight mechanics
Aircraft flight mechanics are relevant to fixed wing ( gliders, aeroplanes) and rotary wing (helicopters) aircraft. An aeroplane (''airplane'' in US usage), is defined in ICAO Document 9110 as, "a power-driven heavier than air aircraft, deriving i ...
as the symbol for
bank angle (sometimes represented with the letter theta, which is also used for pitch angle).
* In combustion engineering,
fuel–air equivalence ratio. The ratio between the actual fuel-air ratio to the stoichiometric fuel-air ratio.
* A sentence in
first-order logic.
* The
Veblen function
In mathematics, the Veblen functions are a hierarchy of normal functions ( continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in . If φ0 is any normal function, then for any non-zero ordinal α, φ ...
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
The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic transcription, phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standa ...
(using the straight-line variant form).
* In
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, φ is often used as shorthand for a
generic act. (Also in uppercase.)
* In
perceptual psychology, the
phi phenomenon
The term phi phenomenon is used in a narrow sense for an apparent motion that is observed if two nearby optical stimuli are presented in alternation with a relatively high frequency. In contrast to beta movement, seen at lower frequencies, the st ...
is the apparent motion caused by the successive viewing of stationary objects, such as the frames of a motion picture.
* In
lexical-functional grammar, the function that maps elements from the
c-structure to the
f-structure.
* In
ecology,
site survival probability
Site most often refers to:
* Archaeological site
* Campsite, a place used for overnight stay in an outdoor area
* Construction site
* Location, a point or an area on the Earth's surface or elsewhere
* Website, a set of related web pages, typically ...
, 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
A bacteriophage (), also known informally as a ''phage'' (), is a duplodnaviria virus that infects and replicates within bacteria and archaea. The term was derived from "bacteria" and the Greek φαγεῖν ('), meaning "to devour". Bacteri ...
** Mϕ is used as an abbreviation for the word
macrophage
Macrophages (abbreviated as M φ, MΦ or MP) ( el, large eaters, from Greek ''μακρός'' (') = large, ''φαγεῖν'' (') = to eat) are a type of white blood cell of the immune system that engulfs and digests pathogens, such as cancer cel ...
The uppercase letter Φ is used as a symbol for:
* The
golden ratio conjugate −0.618... in mathematics.
* The
cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x.
Ev ...
(cdf) of
standard normal distribution in statistics.
* The
magnetic flux
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ( ...
and
electric flux in physics, with subscripts distinguishing the two.
* In
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, Φ is often used as shorthand for a
generic act. (Also in lowercase.)
* A common symbol for the parametrization of a surface in vector
calculus.
* In
Lacanian algebra
Jacques Marie Émile Lacan (, , ; 13 April 1901 – 9 September 1981) was a French psychoanalyst and psychiatrist. Described as "the most controversial psycho-analyst since Freud", Lacan gave yearly seminars in Paris from 1953 to 1981, and ...
, Φ stands for the imaginary phallus and also represents phallic signification; −Φ stands in for castration.
The
diameter symbol
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...
in engineering,
⌀
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
, 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.
* A
Clock signal
In electronics and especially synchronous digital circuits, a clock signal (historically also known as ''logic beat'') oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits.
A clock sign ...
in electronics is often called Phi or uses the symbol.
Computing
In
Unicode, there are multiple forms of the phi letter:
In ordinary Greek text, the character U+03C6 φ is used exclusively, although this character has considerable glyphic variation, sometimes represented with a glyph more like the representative glyph shown for U+03C6 (φ, the "loopy" or "open" form), and less often with a glyph more like the representative glyph shown for U+03D5 (ϕ, the "stroked" or "closed" form).
Because Unicode represents a character in an abstract way, the choice between glyphs is purely a matter of font design. While some Greek typefaces, most notably those in the
Porson family (used widely in editions of classical Greek texts), have a "stroked" glyph in this position (), most other typefaces have "loopy" glyphs. This also applies to the "Didot" (or "''apla''") typefaces employed in most Greek book printing (), as well as the "Neohellenic" typeface often used for ancient texts ().
It is necessary to have the stroked glyph available for some mathematical uses, and U+03D5 GREEK PHI SYMBOL is designed for this function. Prior to Unicode version 3.0 (1998), the glyph assignments in the Unicode code charts were the reverse, and thus older fonts may still show a loopy form
at U+03D5.
For use as a phonetic symbol in
IPA
IPA commonly refers to:
* India pale ale, a style of beer
* International Phonetic Alphabet, a system of phonetic notation
* Isopropyl alcohol, a chemical compound
IPA may also refer to:
Organizations International
* Insolvency Practitioners ...
, Unicode has a separate code point U+0278, LATIN SMALL LETTER PHI, because only the stroked glyph is considered correct in this use. It typically appears in a form adapted to a Latin typographic environment, with a more upright shape than normal Greek letters and with
serif
In typography, a serif () is a small line or stroke regularly attached to the end of a larger stroke in a letter or symbol within a particular font or family of fonts. A typeface or "font family" making use of serifs is called a serif typeface ...
s at the top and bottom.
In HTML/
XHTML, the upper- and lowercase phi
character entity reference
Character or Characters may refer to:
Arts, entertainment, and media Literature
* ''Character'' (novel), a 1936 Dutch novel by Ferdinand Bordewijk
* ''Characters'' (Theophrastus), a classical Greek set of character sketches attributed to The ...
s are
Φ
(Φ) and
φ
(φ), respectively.
In
LaTeX, the math symbols are
\Phi
(
),
\phi
(
), and
\varphi
(
).
The Unicode standard also includes the following variants of phi and phi-like characters:
See also
*
F, f: Ef (Latin)
*
Ф, ф: Ef (Cyrillic)
*
中
中 may refer to:
* 中 (U+4E2D), a Unicode character found in the CJK Unified Ideographs (Unicode block)
* China in general
* Chinese culture in general
* Central District, Taichung, Central District (Mandarin zh, links=no, c=中區, p=Zhōng-Q ...
*
Psi and phi type figurine
*
Փ (Armenian)
*
Deposition (geology)
*
Golden ratio
References
External links
*
*
*
*
{{DEFAULTSORT:Phi (Letter)
Greek letters