Pi (uppercase Π, lowercase π and ϖ; el, πι ) is the sixteenth letter of the
Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as ...
, representing the
voiceless bilabial plosive . In the system of
Greek numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those ...
it has a value of 80. It was derived from the
Phoenician letter
Pe (
). Letters that arose from pi include
Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
P,
Cyrillic
The Cyrillic script ( ), Slavonic script or the Slavic script, is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic, Turkic, Mongolic, Uralic, Caucasian and Iranic-speaking co ...
Pe (П, п),
Coptic pi (Ⲡ, ⲡ), and
Gothic
Gothic or Gothics may refer to:
People and languages
*Goths or Gothic people, the ethnonym of a group of East Germanic tribes
**Gothic language, an extinct East Germanic language spoken by the Goths
**Crimean Gothic, the Gothic language spoken b ...
pairthra (𐍀).
Uppercase Pi
The uppercase letter Π is used as a symbol for:
* In textual criticism, ''
Codex Petropolitanus'', a 9th-century
uncial codex of the
Gospel
Gospel originally meant the Christian message (" the gospel"), but in the 2nd century it came to be used also for the books in which the message was set out. In this sense a gospel can be defined as a loose-knit, episodic narrative of the words a ...
s, now located in
St. Petersburg, Russia.
* In
legal shorthand, it represents a
plaintiff
A plaintiff ( Π in legal shorthand) is the party who initiates a lawsuit (also known as an ''action'') before a court. By doing so, the plaintiff seeks a legal remedy. If this search is successful, the court will issue judgment in favor of t ...
.
In science and engineering:
* The
product operator in mathematics, indicated with
capital pi notation (in analogy to the use of the capital
Sigma as
summation symbol).
* The
osmotic pressure in chemistry.
* The
viscous stress tensor in continuum mechanics and fluid dynamics.
Lowercase Pi
The lowercase letter π is used as a symbol for:
* The mathematical real
transcendental (and thus
irrational)
constant π ≈ 3.14159..., the ratio of a circle's
circumference
In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out ...
to its
diameter
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 f ...
in
Euclidean geometry. The letter "π" is the first letter of the Greek words 'periphery' and 'perimeter', i.e. the circumference.
* The
prime-counting function in mathematics.
*
Homotopy groups in algebraic topology.
* Dimensionless parameters constructed using the
Buckingham π theorem of
dimensional analysis.
* The
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ...
called the
pion (pi meson).
*
Economic profit in microeconomics.
*
Inflation
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
rate in macroeconomics.
* A type of
chemical bond in which the p orbitals overlap, called a
pi bond.
* The natural projection on the
tangent bundle on a
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
.
* The unary operation of
projection in
relational algebra.
* Policy in
reinforcement learning.
*
Polyamory (in the earliest polyamory
pride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory).
History
An early form of pi was
, appearing almost like a
gamma
Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter r ...
with a hook.
Variant pi
Variant pi or "pomega" (
or ϖ) is a
glyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercase
omega
Omega (; capital: Ω, lowercase: ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the twenty-fourth and final letter in the Greek alphabet. In the Greek numeric system/ isopsephy ( gematria), it has a value of 800. The ...
with a
macron, though historically it is simply a
cursive
Cursive (also known as script, among other names) is any style of penmanship in which characters are written joined in a flowing manner, generally for the purpose of making writing faster, in contrast to block letters. It varies in functionali ...
form of pi, with its legs bent inward to meet. It was also used in the
minuscule script. It is a symbol for:
*
Angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
of a
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
in
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
(angular frequency is usually represented by
but this may be confused with
vorticity in a fluid dynamics context).
*
Longitude of pericenter in
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, ...
.
*
Comoving distance in cosmology.
*
Single-scattering albedo Single-scattering albedo is the ratio of scattering efficiency to total extinction efficiency (which is also termed "attenuance", a sum of scattering and absorption). Most often it is defined for small-particle scattering of electromagnetic waves. ...
in
radiative transfer.
*
Mean fitness of a population in
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
.
*
Fundamental weights of a representation (probably to better distinguish from elements
of the Weyl group, than the usual notation
).
* The
lemniscate constant.
Character encodings
The various forms of pi are present in
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
as:
*
*
*
*
*
*
* .
Character encodings tables
* Greek / Coptic Pi
[Unicode Code Charts]
Greek and Coptic (Range: 0370-03FF)
/ref>
* Mathematical Pi
The character encodings in the tables above are intended for use as mathematical symbols. Text written in the Greek language (i.e. words, as opposed to mathematics) should not come from any of the tables on this page, but instead should use the normal Greek letters, which have different code numbers and often a different appearance. Using the mathematical symbols to display words (or vice versa) is likely to result in inconsistent spacing and a clumsy, mismatched appearance.
See also
* П, п – Pe (Cyrillic)
* P, p – Pe (Latin)
* Greek letters used in mathematics, science, and engineering#Ππ (pi)
* Tau
References
{{Reflist
Greek letters