Pi (letter)
Template:Short description Template:Greek Alphabet
Pi (Template:IPAc-en; Ancient Greek Template:Ipa or Template:Ipa, uppercase Π, lowercase π, cursive ϖ; Template:Langx) is the sixteenth letter of the Greek alphabet, representing the voiceless bilabial plosive Template:IPA. 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).<ref>Template:Cite web</ref>
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.<ref>Template:Cite web</ref>
- In mathematical finance, it represents a portfolio.
- The product operator in mathematics, indicated with capital pi notation Template:Math (in analogy to the use of the capital Sigma Template:Math as summation symbol).<ref>Template:Cite web</ref>
- The osmotic pressure in chemistry.<ref>Template:Cite web</ref>
- The viscous stress tensor in continuum mechanics and fluid dynamics.
Lowercase pi
The lowercase letter Template: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,<ref>Template:Cite web</ref> exactly half of the circle constant. The letter "Template:Pi" is the first letter of the Greek words Template:Wikt-lang 'periphery' and Template:Wikt-lang 'perimeter', i.e. the circumference.
- The prime-counting function in mathematics.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>
- Homotopy groups in algebraic topology.
- Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.
- The hadron called the pion (pi meson).<ref>Template:Cite web</ref>
- Often inflation rate in macroeconomics.<ref>Template:Cite web</ref>
- Sometimes profit in microeconomics.
- A type of chemical bond in which the p orbitals overlap, called a pi bond.<ref>Template:Cite web</ref>
- The natural projection on the tangent bundle on a manifold.
- The unary operation of projection in relational algebra.<ref>Template:Cite web</ref>
- 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).<ref>Template:Cite web</ref><ref>Template:Cite web</ref><ref>Template:Cite web</ref><ref>Template:Cite web</ref>
History
An early form of pi was Template:GrGl, appearing almost like a gamma with a hook.<ref>Template:Cite book</ref><ref>Template:Cite book</ref>
Variant pi
Variant pi or "pomega" (<math>\varpi\,\!</math> 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 <math>\omega</math> but this may be confused with vorticity in a fluid dynamics context).
- Longitude of pericenter in celestial mechanics.<ref>Template:Cite web</ref>
- Comoving distance in cosmology.<ref>Outline for Weeks 14&15, Astronomy 225 Spring 2008 Template:Webarchive</ref>
- Single-scattering albedo in radiative transfer.
- Mean fitness of a population in biology.
- Fundamental weights of a representation (probably to better distinguish from elements <math>w</math> of the Weyl group, than the usual notation <math>\omega</math>).
- The lemniscate constant.<ref>Template:Cite journal</ref>
Unicode
Lower-case pi was fairly common in 8-bit character encodings, for instance it is at Template:Tt in CP437 and at Template:Tt on Mac OS Roman. The various forms of pi present in Unicode are:
- Template:Unichar
- Template:Unichar
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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:
- Template:Unichar
- Template:Unichar<ref>Template:Cite web</ref>
- Template:Unichar
- Template:Unichar
- Template:Unichar
- Template:Unichar
- Template:Unichar
- Template:Unichar
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See also
- [[Greek letters used in mathematics, science, and engineering#Ππ (
- П, п – Pe (Cyrillic)
- P, p – Pe (Latin)pi)]]
- Tau