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 we ...
, representing the
voiceless bilabial plosive
The voiceless bilabial plosive or stop is a type of consonantal sound used in most spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is p.
Features
Features o ...
. 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 tho ...
it has a value of 80. It was derived from the
Phoenician letter
Pe (
![Phoenician pe](https://upload.wikimedia.org/wikipedia/commons/8/8b/Phoenician_pe.svg)
). Letters that arose from pi include
Latin
Latin (, or , ) is a classical language belonging to the 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 the power of the ...
P,
Cyrillic
, bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця
, fam1 = Egyptian hieroglyphs
, fam2 = Proto-Sinaitic
, fam3 = Phoenician
, fam4 = G ...
Pe (П, п),
Coptic
Coptic may refer to:
Afro-Asia
* Copts, an ethnoreligious group mainly in the area of modern Egypt but also in Sudan and Libya
* Coptic language, a Northern Afro-Asiatic language spoken in Egypt until at least the 17th century
* Coptic alphabet ...
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
Uncial is a majuscule Glaister, Geoffrey Ashall. (1996) ''Encyclopedia of the Book''. 2nd edn. New Castle, DE, and London: Oak Knoll Press & The British Library
The British Library is the national library of the United Kingdom and is one ...
codex
The codex (plural codices ) was the historical ancestor of the modern book. Instead of being composed of sheets of paper, it used sheets of vellum, papyrus, or other materials. The term ''codex'' is often used for ancient manuscript books, with ...
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 an ...
s, now located in
St. Petersburg, Russia
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
.
* In
legal shorthand
This is a list of abbreviations used in law and legal documents. It is common practice in legal documents to cite other publications by using standard abbreviations for the title of each source. Abbreviations may also be found for common words o ...
, 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 the p ...
.
In science and engineering:
* The
product
Product may refer to:
Business
* Product (business), an item that serves as a solution to a specific consumer problem.
* Product (project management), a deliverable or set of deliverables that contribute to a business solution
Mathematics
* Produ ...
operator in mathematics, indicated with
capital pi notation
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additio ...
(in analogy to the use of the capital
Sigma as
summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, mat ...
symbol).
* The
osmotic pressure in chemistry.
* The
viscous stress tensor
The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed to the strain rate, the rate at which it is deforming around that point.
The viscous stress ...
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
Irrationality is cognition, thinking, talking, or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. T ...
)
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 t ...
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 for ...
in
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small ...
. 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
In engineering, applied mathematics, and physics, the Buckingham theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically me ...
of
dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as mi ...
.
* 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 e ...
called the
pion
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more gene ...
(pi meson).
*
Economic profit
In economics, profit is the difference between the revenue that an economic entity has received from its outputs and the total cost of its inputs. It is equal to total revenue minus total cost, including both explicit and implicit costs.
It ...
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
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
in which the p orbitals overlap, called a
pi bond
In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals ...
.
* The natural projection on the
tangent bundle
In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M . As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points and of ...
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
Projection, projections or projective may refer to:
Physics
* Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction
* The display of images by a projector
Optics, graphic ...
in
relational algebra
In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. The theory was introduced by Edgar F. Codd.
The main application of relational algebr ...
.
* Policy in
reinforcement learning
Reinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine ...
.
![Polyamory Pride Flag](https://upload.wikimedia.org/wikipedia/commons/b/b6/Polyamory_Pride_Flag.svg)
*
Polyamory
Polyamory () is the practice of, or desire for, romantic relationships with more than one partner at the same time, with the informed consent of all partners involved. People who identify as polyamorous may believe in open relationships wi ...
(in the earliest polyamory
pride flag
A pride flag is any flag that represents a segment or part of the LGBT community. ''Pride'' in this case refers to the notion of gay pride. The terms ''LGBT flag'' and ''queer flag'' are often used interchangeably.
The rainbow flag is the most ...
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 with a hook.
Variant pi
Variant pi or "pomega" (
or ϖ) is a
glyph
A glyph () is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface, of an element of written language. A g ...
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 wo ...
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 functionalit ...
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 tim ...
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 (res ...
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) an ...
(angular frequency is usually represented by
but this may be confused with
vorticity
In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wi ...
in a fluid dynamics context).
*
Longitude of pericenter
In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) woul ...
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, to ...
.
*
Comoving distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...
in cosmology.
*
Single-scattering albedo in
radiative transfer
Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative trans ...
.
*
Mean fitness
Fitness (often denoted w or ω in population genetics models) is the quantitative representation of individual reproductive success. It is also equal to the average contribution to the gene pool of the next generation, made by the same individu ...
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 i ...
.
*
Fundamental weights of a representation (probably to better distinguish from elements
of the Weyl group, than the usual notation
).
* The
lemniscate constant
In mathematics, the lemniscate constant p. 199 is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of for the circle. Equivalently, the perimeter ...
.
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 Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ...
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
Tau (uppercase Τ, lowercase τ, or \boldsymbol\tau; el, ταυ ) is the 19th letter of the Greek alphabet, representing the voiceless dental or alveolar plosive . In the system of Greek numerals, it has a value of 300.
The name in English ...
References
{{Reflist
Greek letters