Pi (letter)

The uppercase letter Π is used as a symbol for:

• In textual criticism, Codex Petropolitanus, a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia.
• In legal shorthand, it represents a plaintiff.{{Cite web |last=sinclair |date=2024-01-22 |title=The Top Legal Symbol Keyboard Shortcuts You Should Know |url=https://lawrank.com/top-legal-keyboard-shortcuts/ |access-date=2025-01-18 |website=LawRank |language=en-US |quote=If you work with plaintiffs, you may choose to replace the word “plaintiff” with a symbol in some of your writing. The plaintiff symbol looks like the Greek letter pi (π).}}
• In Mathematical finance, it represents a portfolio.

In science and engineering:

• The product operator in mathematics, indicated with capital pi notation {{Math|Π}} (in analogy to the use of the capital Sigma {{Math|Σ}} as summation symbol).{{Cite web |last=Weisstein |first=Eric W. |title=Product |url=https://mathworld.wolfram.com/Product.html |access-date=2025-01-18 |website=mathworld.wolfram.com |language=en}}
• The osmotic pressure in chemistry.{{Cite web |date=2015-01-18 |title=13.7: Osmotic Pressure |url=https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:_General_Chemistry_(Petrucci_et_al.)/13:_Solutions_and_their_Physical_Properties/13.07:_Osmotic_Pressure |access-date=2025-01-18 |website=Chemistry LibreTexts |language=en}}
• The viscous stress tensor in continuum mechanics and fluid dynamics.

The lowercase letter {{pi}} is used as a symbol for:

• The mathematical real transcendental (and thus irrational) constant π ≈ 3.14159..., the ratio of a circle's circumference to its diameter in Euclidean geometry,{{Cite web |last=Weisstein |first=Eric W. |title=Pi |url=https://mathworld.wolfram.com/Pi.html |access-date=2025-01-18 |website=mathworld.wolfram.com |language=en |quote=The constant pi, denoted {{pi}}, is a real number defined as the ratio of a circle's circumference C to its diameter}} exactly half of the circle constant. The letter "{{pi}}" is the first letter of the Greek words {{wikt-lang|grc|περιφέρεια}} 'periphery' and {{wikt-lang|grc|περίμετρος}} 'perimeter', i.e. the circumference.
• The prime-counting function in mathematics.{{Cite web |last=Weisstein |first=Eric W. |title=Prime Counting Function |url=https://mathworld.wolfram.com/PrimeCountingFunction.html |access-date=2025-01-18 |website=mathworld.wolfram.com |language=en |quote=The prime counting function is the function {{pi}}(x) giving the number of primes less than or equal to...}}{{Cite web |title=DLMF: §27.12 Asymptotic Formulas: Primes ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory |url=https://dlmf.nist.gov/27.12 |access-date=2025-01-31 |website=dlmf.nist.gov}}
• Homotopy groups in algebraic topology.
• Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.
• The hadron called the pion (pi meson).{{Cite web |title=Pi meson {{!}} subatomic particle {{!}} Britannica |url=https://www.britannica.com/science/pi-meson |access-date=2025-01-18 |website=www.britannica.com |language=en |quote=Also known as: pion}}
• Often inflation rate in macroeconomics.{{Cite web |title=Fisher Equation |url=https://corporatefinanceinstitute.com/resources/economics/fisher-equation/ |access-date=2025-01-18 |website=Corporate Finance Institute |language=en-US |quote=π – the inflation rate}}
• Sometimes profit in microeconomics.
• A type of chemical bond in which the p orbitals overlap, called a pi bond.{{Cite web |title=Pi bond {{!}} Double Bond, Electron Sharing & Hybridization {{!}} Britannica |url=https://www.britannica.com/science/pi-bond |access-date=2025-01-18 |website=www.britannica.com |language=en}}
• The natural projection on the tangent bundle on a manifold.
• The unary operation of projection in relational algebra.{{Cite web |date=2024-03-25 |title=What are the Unary Operations in Relational Algebra? |url=https://www.geeksforgeeks.org/what-are-the-unary-operations-in-relational-algebra/ |access-date=2025-01-18 |website=GeeksforGeeks |language=en-US |quote=The projection operation is a unary operation that is performed on a relation. A projection operation is used to retrieve all the values of one or more attributes. It is denoted by π.}}
• Policy in reinforcement learning.

File:Polyamory Pride Flag.svg pride flag design, created by Jim Evans in 1995, in which the lowercase letter π stands for the first letter of polyamory.]]

• Polyamory (in the earliest polyamory pride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory).{{Cite web|url=https://www.thespinoff.co.nz/society/22-04-2019/pretty-poly-why-non-monogamous-relationships-are-all-the-rage/|title=Pretty poly: Why non-monogamous relationships are all the rage|first=Melody|last=Thomas|date=April 22, 2019|access-date=March 24, 2021|archive-date=February 26, 2021|archive-url=https://web.archive.org/web/20210226022106/https://thespinoff.co.nz/society/22-04-2019/pretty-poly-why-non-monogamous-relationships-are-all-the-rage/|url-status=live}}{{Cite web|url=https://www.goodhousekeeping.com/life/g39944774/lgbtq-flags/|title=21 LGBTQ Flags and What They Symbolize|first=Lizz|last=Schumer|date=May 16, 2022|website=Good Housekeeping}}{{Cite web|url=https://www.lgbtqnation.com/2022/06/polyamorous-flag-look-like/|title=What does the polyamorous flag look like?|first=Matthias|last=Walsh|website=LGBTQ Nation|date=17 June 2022 }}{{cite web|title=Jim Evans' Polyamory Pride Flag|url=http://homepage.isomedia.com/~jene/flag.html|archive-url=https://web.archive.org/web/20141110021410/http://homepage.isomedia.com/~jene/flag.html|archive-date=November 10, 2014}}

An early form of pi was {{GrGl|Pi archaic}}, appearing almost like a gamma with a hook.{{Cite book |last=Thompson |first=Edward Maunde |url=https://www.cambridge.org/core/books/an-introduction-to-greek-and-latin-palaeography/4E5810810D8AEE5ED461584112ACA4FE |title=An Introduction to Greek and Latin Palaeography |date=2013 |orig-date=1912|publisher=Cambridge University Press |isbn=978-1-108-06181-0 |series=Cambridge Library Collection - Classics |location=Cambridge |doi=10.1017/cbo9781139833790}}{{Cite book |last=Faulmann |first=Karl |title=Schriftzeichen und Alphabete aller Zeiten und Völker |date=2000 |publisher=Augustus |isbn=978-3-8043-0374-4 |edition=Repr. nach d. Wiener Ausg. 1880, Neuausg |location=München|lang=German}}

Variant pi or "pomega" ($\backslash varpi\backslash ,\backslash !$ or ϖ) is a glyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercase omega with a macron, though historically it is simply a cursive 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 of a wave in fluid dynamics (angular frequency is usually represented by $\backslash omega$ but this may be confused with vorticity in a fluid dynamics context).
• Longitude of pericenter in celestial mechanics.{{cite web |url=http://scienceworld.wolfram.com/physics/Pomega.html |title=Pomega |work=Eric Weisstein's World of Physics |publisher=wolfram.com}}
• Comoving distance in cosmology.[http://odin.physastro.mnsu.edu/~eskridge/astr225/week14.html Outline for Weeks 14&15, Astronomy 225 Spring 2008] {{webarchive|url=https://web.archive.org/web/20100615221333/http://odin.physastro.mnsu.edu/~eskridge/astr225/week14.html |date=2010-06-15 }}
• Single-scattering albedo in radiative transfer.
• Mean fitness of a population in biology.
• Fundamental weights of a representation (probably to better distinguish from elements $w$ of the Weyl group, than the usual notation $\backslash omega$).
• The lemniscate constant.{{cite journal |last1=Kobayashi |first1=Hiroyuki |last2=Takeuchi |first2=Shingo |title=Applications of generalized trigonometric functions with two parameters |journal=Communications on Pure & Applied Analysis |date=2019 |volume=18 |issue=3 |pages=1509 |doi=10.3934/cpaa.2019072|arxiv=1903.07407|s2cid=102487670 }}

Lower-case pi was fairly common in 8-bit character encodings, for instance it is at {{tt|0xE3}} in CP437 and at {{tt|0xB9}} on Mac OS Roman.

The various forms of pi present in Unicode are:

• {{unichar|03A0|GREEK CAPITAL LETTER PI|html=}}
• {{unichar|03C0|GREEK SMALL LETTER PI|html=}}
• {{unichar|03D6|GREEK PI SYMBOL|html=}}
• {{unichar|1D28|GREEK LETTER SMALL CAPITAL PI|html=}}
• {{unichar|213F}}
• {{unichar|213C}}
• {{unichar|220F|html=}}
• {{unichar|2210|html=}}
• {{unichar|2CA0}}
• {{unichar|2CA1}}

These 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:

• {{unichar|1D6B7}}
• {{unichar|1D6D1}}{{cite web|url=https://www.fileformat.info/info/unicode/font/calibri/list.htm|title=Unicode characters supported by the Calibri font|work=fileformat.info}}
• {{unichar|1D6E1}}
• {{unichar|1D6F1}}
• {{unichar|1D70B}}
• {{unichar|1D71B}}
• {{unichar|1D72B}}
• {{unichar|1D745}}
• {{unichar|1D755}}
• {{unichar|1D765}}
• {{unichar|1D77F}}
• {{unichar|1D78F}}
• {{unichar|1D79F}}
• {{unichar|1D7B9}}
• {{unichar|1D7C9}}

{{Wiktionary|Π|π}}

• П, п – Pe (Cyrillic)
• P, p – Pe (Latin)
• Greek letters used in mathematics, science, and engineering#Ππ (pi)
• Tau

{{Reflist}}

Category:Greek letters