Pi (letter)

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

Sixteenth letter in the Greek alphabet

Greek alphabet
|  Αα|  Alpha|  Νν|  Nu

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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
History

Archaic local variants

* Ϝ
* Ͱ
* Ϻ
* Ϙ
* Ͳ
* Ͷ

* tsan
* digamma

* Diacritics
* Ligatures

Numerals

* ϛ (6)
* ϟ (90)
* ϡ (900)

Use in other languages

* Bactrian
* Coptic
* Albanian

Related topics

* Use as scientific symbols

* Category

* v
* t
* e

Pi (/ˈpaɪ/; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive ϖ; Greek: πι [pi]) is the sixteenth letter of the Greek alphabet, meaning units united, and representing the voiceless bilabial plosive IPA: [p]. In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter Pe (). Letters that arose from pi include Latin P, Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).[1]

## Uppercase Pi[edit]

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.

In science and engineering:

* The product operator in mathematics, indicated with capital pi notation Π (in analogy to the use of the capital Sigma Σ as summation symbol).
* The osmotic pressure in chemistry.
* The viscous stress tensor in continuum mechanics and fluid dynamics.

## Lowercase Pi[edit]

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 to its diameter in Euclidean geometry. The letter "π" is the first letter of the Greek words περιφέρεια 'periphery' and περίμετρος '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 called the pion (pi meson).
* Often inflation rate in macroeconomics.
* Sometimes profit in microeconomics.
* 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.
* The unary operation of projection in relational algebra.
* Policy in reinforcement learning.

The earliest polyamory 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).[2][3][4][5]

## History[edit]

An early form of pi was , appearing almost like a gamma with a hook.

## Variant pi[edit]

Variant pi or "pomega" ( ϖ {\displaystyle \varpi \,\\!} 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  ω {\displaystyle \omega } but this may be confused with vorticity in a fluid dynamics context).
* Longitude of pericenter in celestial mechanics.[6]
* Comoving distance in cosmology.[7]
* 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 {\displaystyle w} of the Weyl group, than the usual notation  ω {\displaystyle \omega } ).
* The lemniscate constant.[8]

## Character encodings[edit]

The various forms of pi are present in Unicode as:

* U+03A0 Π GREEK CAPITAL LETTER PI (&Pi;)
* U+03C0 π GREEK SMALL LETTER PI (&pi;)
* U+03D6 ϖ GREEK PI SYMBOL (&piv;, &varpi;)
* U+220F ∏ N-ARY PRODUCT (&prod;, &Product;)
* U+1D28 ᴨ GREEK LETTER SMALL CAPITAL PI
* U+1D70B 𝜋 MATHEMATICAL ITALIC SMALL PI
* U+1D6D1 𝛑 MATHEMATICAL BOLD SMALL PI.[9]

### Character encodings tables[edit]

* Greek / Coptic Pi[10]

Character information  Preview | Π | π | ϖ | Ⲡ | ⲡ

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Unicode name  | GREEK CAPITAL LETTER PI  | GREEK SMALL LETTER PI  | GREEK PI SYMBOL  | COPTIC CAPITAL LETTER PI  | COPTIC SMALL LETTER PI
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex
Unicode | 928 | U+03A0 | 960 | U+03C0 | 982 | U+03D6 | 11424 | U+2CA0 | 11425 | U+2CA1
UTF-8 | 206 160 | CE A0 | 207 128 | CF 80 | 207 150 | CF 96 | 226 178 160 | E2 B2 A0 | 226 178 161 | E2 B2 A1
Numeric character reference | &#928; | &#x3A0; | &#960; | &#x3C0; | &#982; | &#x3D6; | &#11424; | &#x2CA0; | &#11425; | &#x2CA1;
Named character reference | &Pi; | &pi; | &piv;, &varpi; |  |
DOS Greek | 143 | 8F | 167 | A7 |  |  |  |  |  |
DOS Greek-2 | 198 | C6 | 234 | EA |  |  |  |  |  |
Windows 1253 | 208 | D0 | 240 | F0 |  |  |  |  |  |
TeX | \Pi | \pi | \varpi |  |
* Mathematical Pi

Character information  Preview | ∏ | ∐ | 𝚷 | 𝛑 | 𝛱 | 𝜋

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Unicode name  | N-ARY PRODUCT  | N-ARY COPRODUCT  | MATHEMATICAL BOLD
CAPITAL PI  | MATHEMATICAL BOLD
SMALL PI  | MATHEMATICAL ITALIC
CAPITAL PI  | MATHEMATICAL ITALIC
SMALL PI
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex
Unicode | 8719 | U+220F | 8720 | U+2210 | 120503 | U+1D6B7 | 120529 | U+1D6D1 | 120561 | U+1D6F1 | 120587 | U+1D70B
UTF-8 | 226 136 143 | E2 88 8F | 226 136 144 | E2 88 90 | 240 157 154 183 | F0 9D 9A B7 | 240 157 155 145 | F0 9D 9B 91 | 240 157 155 177 | F0 9D 9B B1 | 240 157 156 139 | F0 9D 9C 8B
UTF-16 | 8719 | 220F | 8720 | 2210 | 55349 57015 | D835 DEB7 | 55349 57041 | D835 DED1 | 55349 57073 | D835 DEF1 | 55349 57099 | D835 DF0B
Numeric character reference | &#8719; | &#x220F; | &#8720; | &#x2210; | &#120503; | &#x1D6B7; | &#120529; | &#x1D6D1; | &#120561; | &#x1D6F1; | &#120587; | &#x1D70B;
Named character reference | &prod;, &Product; | &coprod;, &Coproduct; |  |  |  |
TeX | \prod | \coprod |  |  |  |

Character information  Preview | 𝜫 | 𝝅 | 𝝥 | 𝝿 | 𝞟 | 𝞹

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Unicode name  | MATHEMATICAL BOLD ITALIC
CAPITAL PI  | MATHEMATICAL BOLD ITALIC
SMALL PI  | MATHEMATICAL SANS-SERIF
BOLD CAPITAL PI  | MATHEMATICAL SANS-SERIF
BOLD SMALL PI  | MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL PI  | MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL PI
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex
Unicode | 120619 | U+1D72B | 120645 | U+1D745 | 120677 | U+1D765 | 120703 | U+1D77F | 120735 | U+1D79F | 120761 | U+1D7B9
UTF-8 | 240 157 156 171 | F0 9D 9C AB | 240 157 157 133 | F0 9D 9D 85 | 240 157 157 165 | F0 9D 9D A5 | 240 157 157 191 | F0 9D 9D BF | 240 157 158 159 | F0 9D 9E 9F | 240 157 158 185 | F0 9D 9E B9
UTF-16 | 55349 57131 | D835 DF2B | 55349 57157 | D835 DF45 | 55349 57189 | D835 DF65 | 55349 57215 | D835 DF7F | 55349 57247 | D835 DF9F | 55349 57273 | D835 DFB9
Numeric character reference | &#120619; | &#x1D72B; | &#120645; | &#x1D745; | &#120677; | &#x1D765; | &#120703; | &#x1D77F; | &#120735; | &#x1D79F; | &#120761; | &#x1D7B9;

Character information  Preview | ℿ | ℼ

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Unicode name  | DOUBLE-STRUCK CAPITAL PI  | DOUBLE-STRUCK SMALL PI
Encodings | decimal | hex | dec | hex
Unicode | 8511 | U+213F | 8508 | U+213C
UTF-8 | 226 132 191 | E2 84 BF | 226 132 188 | E2 84 BC
Numeric character reference | &#8511; | &#x213F; | &#8508; | &#x213C;
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[edit]

Look up Π or π in Wiktionary, the free dictionary.

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

## References[edit]

1. ^ "Pi Symbol in Greek Alphabet". greeksymbols.net. Retrieved 2023-02-07.
2. ^ Thomas, Melody (April 22, 2019). "Pretty poly: Why non-monogamous relationships are all the rage". Archived from the original on February 26, 2021. Retrieved March 24, 2021.
3. ^ Schumer, Lizz (May 16, 2022). "21 LGBTQ Flags and What They Symbolize". Good Housekeeping.
4. ^ Walsh, Matthias. "What does the polyamorous flag look like?". LGBTQ Nation.
5. ^ "Jim Evans' Polyamory Pride Flag". Archived from the original on November 10, 2014.
6. ^ "Pomega". Eric Weisstein's World of Physics. wolfram.com.
7. ^ Outline for Weeks 14&15, Astronomy 225 Spring 2008 Archived 2010-06-15 at the Wayback Machine
8. ^ 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.
9. ^ "Unicode characters supported by the Calibri font". fileformat.info.
10. ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)

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