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Pi (letter)

From Wikipedia, the free encyclopedia

This article is about a Greek letter. For the number symbolized by this letter, seePi.

Greek letter

Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega

Archaic local variants

Ϝϝ	Digamma	Ͱͱ	Heta
Ϻϻ	San	Ϙϙ	Koppa
Ͷͷ	Tsan Digamma	Ͳͳ	Sampi
Ϸϸ	Sho

Diacritics and other symbols

Numerals (Attic)

Related topics

Category

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Pi (/ˈpaɪ/ ^ⓘ;Ancient Greek /piː/ or /peî/, uppercaseΠ, lowercaseπ,cursiveϖ;Greek:πι) is the sixteenth letter of theGreek alphabet, representing thevoiceless bilabial plosiveIPA:[p]. In the system ofGreek numerals it has a value of 80. It was derived from thePhoenician letterPe (). Letters that arose from pi includeLatin P,Cyrillic Pe (П, п),Coptic pi (Ⲡ, ⲡ), andGothic pairthra (𐍀).^[1]

Uppercase Pi

The uppercase letter Π is used as a symbol for:

In textual criticism,Codex Petropolitanus, a 9th-centuryuncial codex of theGospels, now located inSt. Petersburg, Russia.
Inlegal shorthand, it represents aplaintiff.^[2]
InMathematical finance, it represents a portfolio.

In science and engineering:

Theproduct operator in mathematics, indicated withcapital pi notationΠ (in analogy to the use of the capitalSigmaΣ assummation symbol).^[3]
Theosmotic pressure in chemistry.^[4]
Theviscous stress tensor in continuum mechanics and fluid dynamics.

Lowercase Pi

The lowercase letterπ is used as a symbol for:

The mathematical realtranscendental (and thusirrational)constant π ≈ 3.14159..., the ratio of a circle'scircumference to itsdiameter inEuclidean geometry,^[5] exactly half of the circle constant. The letter "π" is the first letter of the Greek wordsπεριφέρεια 'periphery' andπερίμετρος 'perimeter', i.e. the circumference.
Theprime-counting function in mathematics.^[6]^[7]
Homotopy groups in algebraic topology.
Dimensionless parameters constructed using theBuckingham π theorem ofdimensional analysis.
Thehadron called thepion (pi meson).^[8]
Ofteninflation rate in macroeconomics.^[9]
Sometimesprofit in microeconomics.
A type ofchemical bond in which the p orbitals overlap, called api bond.^[10]
The natural projection on thetangent bundle on amanifold.
The unary operation ofprojection inrelational algebra.^[11]
Policy inreinforcement learning.

The earliestpolyamory 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 polyamorypride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory).^[12]^[13]^[14]^[15]

History

An early form of pi was, appearing almost like agamma with a hook.^[16]^[17]

Variant pi

Variant pi or "pomega" ( $\varpi \,\!$ or ϖ) is aglyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercaseomega with amacron, though historically it is simply acursive form of pi, with its legs bent inward to meet. It was also used in theminuscule script. It is a symbol for:

Angular frequency of awave influid dynamics (angular frequency is usually represented by $\omega$ but this may be confused withvorticity in a fluid dynamics context).
Longitude of pericenter incelestial mechanics.^[18]
Comoving distance in cosmology.^[19]
Single-scattering albedo inradiative transfer.
Mean fitness of a population inbiology.
Fundamental weights of a representation (probably to better distinguish from elements $w {\displaystyle w}$ of the Weyl group, than the usual notation $\omega$ ).
Thelemniscate constant.^[20]

Unicode

Lower-case pi was fairly common in 8-bit character encodings, for instance it is at0xE3 inCP437 and at0xB9 onMac OS Roman.The various forms of pi present inUnicode are:

U+03A0 ΠGREEK CAPITAL LETTER PI (Π)
U+03C0 πGREEK SMALL LETTER PI (π)
U+03D6 ϖGREEK PI SYMBOL (ϖ, ϖ)
U+1D28 ᴨGREEK LETTER SMALL CAPITAL PI
U+213F ℿDOUBLE-STRUCK CAPITAL PI
U+213C ℼDOUBLE-STRUCK SMALL PI
U+220F ∏N-ARY PRODUCT (∏, &Product;)
U+2210 ∐N-ARY COPRODUCT (&coprod;, &Coproduct;)
U+2CA0 ⲠCOPTIC CAPITAL LETTER PI
U+2CA1 ⲡCOPTIC SMALL LETTER PI

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:

U+1D6B7 𝚷MATHEMATICAL BOLD CAPITAL PI
U+1D6D1 𝛑MATHEMATICAL BOLD SMALL PI^[21]
U+1D6E1 𝛡MATHEMATICAL BOLD PI SYMBOL
U+1D6F1 𝛱MATHEMATICAL ITALIC CAPITAL PI
U+1D70B 𝜋MATHEMATICAL ITALIC SMALL PI
U+1D71B 𝜛MATHEMATICAL ITALIC PI SYMBOL
U+1D72B 𝜫MATHEMATICAL BOLD ITALIC CAPITAL PI
U+1D745 𝝅MATHEMATICAL BOLD ITALIC SMALL PI
U+1D755 𝝕MATHEMATICAL BOLD ITALIC PI SYMBOL
U+1D765 𝝥MATHEMATICAL SANS-SERIF BOLD CAPITAL PI
U+1D77F 𝝿MATHEMATICAL SANS-SERIF BOLD SMALL PI
U+1D78F 𝞏MATHEMATICAL SANS-SERIF BOLD PI SYMBOL
U+1D79F 𝞟MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PI
U+1D7B9 𝞹MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PI
U+1D7C9 𝟉MATHEMATICAL SANS-SERIF BOLD ITALIC PI SYMBOL

See also

Look upΠ orπ in Wiktionary, the free dictionary.

References

^"Pi Symbol in Greek Alphabet".greeksymbols.net. Retrieved2023-02-07.
^sinclair (2024-01-22)."The Top Legal Symbol Keyboard Shortcuts You Should Know".LawRank. Retrieved2025-01-18.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).
^Weisstein, Eric W."Product".mathworld.wolfram.com. Retrieved2025-01-18.
^"13.7: Osmotic Pressure".Chemistry LibreTexts. 2015-01-18. Retrieved2025-01-18.
^Weisstein, Eric W."Pi".mathworld.wolfram.com. Retrieved2025-01-18.The constant pi, denotedπ, is a real number defined as the ratio of a circle's circumference C to its diameter
^Weisstein, Eric W."Prime Counting Function".mathworld.wolfram.com. Retrieved2025-01-18.The prime counting function is the functionπ(x) giving the number of primes less than or equal to...
^"DLMF: §27.12 Asymptotic Formulas: Primes ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory".dlmf.nist.gov. Retrieved2025-01-31.
^"Pi meson | subatomic particle | Britannica".www.britannica.com. Retrieved2025-01-18.Also known as: pion
^"Fisher Equation".Corporate Finance Institute. Retrieved2025-01-18.π – the inflation rate
^"Pi bond | Double Bond, Electron Sharing & Hybridization | Britannica".www.britannica.com. Retrieved2025-01-18.
^"What are the Unary Operations in Relational Algebra?".GeeksforGeeks. 2024-03-25. Retrieved2025-01-18.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.
^Thomas, Melody (April 22, 2019)."Pretty poly: Why non-monogamous relationships are all the rage".Archived from the original on February 26, 2021. RetrievedMarch 24, 2021.
^Schumer, Lizz (May 16, 2022)."21 LGBTQ Flags and What They Symbolize".Good Housekeeping.
^Walsh, Matthias (17 June 2022)."What does the polyamorous flag look like?".LGBTQ Nation.
^"Jim Evans' Polyamory Pride Flag". Archived fromthe original on November 10, 2014.
^Thompson, Edward Maunde (2013) [1912].An Introduction to Greek and Latin Palaeography. Cambridge Library Collection - Classics. Cambridge: Cambridge University Press.doi:10.1017/cbo9781139833790.ISBN 978-1-108-06181-0.
^Faulmann, Karl (2000).Schriftzeichen und Alphabete aller Zeiten und Völker (in German) (Repr. nach d. Wiener Ausg. 1880, Neuausg ed.). München: Augustus.ISBN 978-3-8043-0374-4.
^"Pomega".Eric Weisstein's World of Physics. wolfram.com.
^Outline for Weeks 14&15, Astronomy 225 Spring 2008 Archived 2010-06-15 at theWayback Machine
^Kobayashi, Hiroyuki; Takeuchi, Shingo (2019). "Applications of generalized trigonometric functions with two parameters".Communications on Pure & Applied Analysis.18 (3): 1509.arXiv:1903.07407.doi:10.3934/cpaa.2019072.S2CID 102487670.
^"Unicode characters supported by the Calibri font".fileformat.info.

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