Pi (letter)
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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 Mathematical finance, it represents a portfolio.
- 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, exactly half of the circle constant. 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.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Polyamory_Pride_Flag.svg/220px-Polyamory_Pride_Flag.svg.png)
- 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]![]() | This section needs expansion. You can help by adding to it. (March 2024) |
An early form of pi was , appearing almost like a gamma with a hook.[6][7]
Variant pi
[edit]Variant pi or "pomega" ( 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 but this may be confused with vorticity in a fluid dynamics context).
- Longitude of pericenter in celestial mechanics.[8]
- Comoving distance in cosmology.[9]
- Single-scattering albedo in radiative transfer.
- Mean fitness of a population in biology.
- Fundamental weights of a representation (probably to better distinguish from elements of the Weyl group, than the usual notation ).
- The lemniscate constant.[10]
Character encodings
[edit]The various forms of pi are present in Unicode as:
- U+03A0 Π GREEK CAPITAL LETTER PI (Π)
- U+03C0 π GREEK SMALL LETTER PI (π)
- U+03D6 ϖ GREEK PI SYMBOL (ϖ, ϖ)
- U+220F ∏ N-ARY PRODUCT (∏, ∏)
- U+1D28 ᴨ GREEK LETTER SMALL CAPITAL PI
- U+1D70B 𝜋 MATHEMATICAL ITALIC SMALL PI
- U+1D6D1 𝛑 MATHEMATICAL BOLD SMALL PI.[11]
Character encodings tables
[edit]- Greek / Coptic Pi[12]
Character information Preview Π π ϖ Ⲡ ⲡ 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 Π Π π π ϖ ϖ Ⲡ Ⲡ ⲡ ⲡ Named character reference Π π ϖ, ϖ 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 Unicode name N-ARY PRODUCT N-ARY COPRODUCT MATHEMATICAL BOLD
CAPITAL PIMATHEMATICAL BOLD
SMALL PIMATHEMATICAL ITALIC
CAPITAL PIMATHEMATICAL ITALIC
SMALL PIEncodings 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 ∏ ∏ ∐ ∐ 𝚷 𝚷 𝛑 𝛑 𝛱 𝛱 𝜋 𝜋 Named character reference ∏, ∏ ∐, ∐ TeX \prod \coprod
Character information Preview 𝜫 𝝅 𝝥 𝝿 𝞟 𝞹 Unicode name MATHEMATICAL BOLD ITALIC
CAPITAL PIMATHEMATICAL BOLD ITALIC
SMALL PIMATHEMATICAL SANS-SERIF
BOLD CAPITAL PIMATHEMATICAL SANS-SERIF
BOLD SMALL PIMATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL PIMATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL PIEncodings 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 𝜫 𝜫 𝝅 𝝅 𝝥 𝝥 𝝿 𝝿 𝞟 𝞟 𝞹 𝞹
Character information Preview ℿ ℼ 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 ℿ ℿ ℼ ℼ
See also
[edit]- П, п – Pe (Cyrillic)
- P, p – Pe (Latin)
- Greek letters used in mathematics, science, and engineering#Ππ (pi)
- Tau
References
[edit]- ^ "Pi Symbol in Greek Alphabet". greeksymbols.net. Retrieved 2023-02-07.
- ^ 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.
- ^ Schumer, Lizz (May 16, 2022). "21 LGBTQ Flags and What They Symbolize". Good Housekeeping.
- ^ Walsh, Matthias. "What does the polyamorous flag look like?". LGBTQ Nation.
- ^ "Jim Evans' Polyamory Pride Flag". Archived from the 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 the Wayback 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.
- ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)