Pi (letter) explained

Pi (/ˈpaɪ/; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive ϖ; Greek, Modern (1453-);: πι in Greek, Modern (1453-); pronounced as /pi/) is the sixteenth letter of the Greek alphabet, meaning units united, and representing the voiceless bilabial plosive in Greek, Modern (1453-); pronounced as /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 .^[1]

Uppercase Pi

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.

In science and engineering

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

Lowercase Pi

The lowercase letter 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 "" 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 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.

• 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

An early form of pi was

, appearing almost like a gamma with a hook.^{[6] [7]}

Variant pi

Variant pi or "pomega" (

\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

\omega 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

w of the Weyl group, than the usual notation \omega ).

• The lemniscate constant.^[10]

Character encodings

The various forms of pi are present in Unicode as:

• • • • • • • .^[11]

Character encodings tables

See also

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

Notes and References

1. Web site: Pi Symbol in Greek Alphabet . 2023-02-07 . greeksymbols.net . en.
2. Web site: Pretty poly: Why non-monogamous relationships are all the rage. Melody. Thomas. April 22, 2019. March 24, 2021. February 26, 2021. https://web.archive.org/web/20210226022106/https://thespinoff.co.nz/society/22-04-2019/pretty-poly-why-non-monogamous-relationships-are-all-the-rage/. live.
3. Web site: 21 LGBTQ Flags and What They Symbolize. Lizz. Schumer. May 16, 2022. Good Housekeeping.
4. Web site: What does the polyamorous flag look like?. Matthias. Walsh. LGBTQ Nation.
5. Web site: Jim Evans' Polyamory Pride Flag. https://web.archive.org/web/20141110021410/http://homepage.isomedia.com/~jene/flag.html. November 10, 2014.
6. Book: Thompson, Edward Maunde . An Introduction to Greek and Latin Palaeography . 2013 . 1912. Cambridge University Press . 978-1-108-06181-0 . Cambridge Library Collection - Classics . Cambridge . 10.1017/cbo9781139833790.
7. Book: Faulmann, Karl . Schriftzeichen und Alphabete aller Zeiten und Völker . 2000 . Augustus . 978-3-8043-0374-4 . Repr. nach d. Wiener Ausg. 1880, Neuausg . München. German.
8. Web site: Pomega . Eric Weisstein's World of Physics . wolfram.com.
9. http://odin.physastro.mnsu.edu/~eskridge/astr225/week14.html Outline for Weeks 14&15, Astronomy 225 Spring 2008
10. Kobayashi . Hiroyuki . Takeuchi . Shingo . Applications of generalized trigonometric functions with two parameters . Communications on Pure & Applied Analysis . 2019 . 18 . 3 . 1509 . 10.3934/cpaa.2019072. 1903.07407. 102487670 .
11. Web site: Unicode characters supported by the Calibri font. fileformat.info.