Pi (letter)

Pi (uppercase Π, lower case π) is the sixteenth letter of the Greek alphabet. In the system of Greek numerals it has a value of 80.

In Modern Greek, the name of the letter is pronEng|pi; in modern English, it is pronounced IPA|/paɪ/, in particular when referring to the mathematical constant (see below). In Greek the letter is pronounced IPA|/p/.

The upper-case letter Π is used as a symbol for:
* The product operator in mathematics, indicated with capital pi notation ∏ (in analogy to the use of the capital Sigma Σ as summation symbol).
* 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.

The lower-case letter π is used as a symbol for:
* The mathematical 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.
* Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.
* The osmotic pressure in chemistry. π=MRT
* The elementary particle called the pi meson or pion.
* Profit in microeconomics.
* Inflation rate in macroeconomics.
* A type of chemical bond in which the P-orbitals overlap
* The natural projection on the tangent bundle on a manifold.

Variant pi or "pomega" ($varpi,!$ or ϖ) is a glyph variant of lower case pi sometimes used in technical contexts as though it were a lower-case omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It is used as a symbol for:
* The 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).
* The longitude of pericenter in celestial mechanics. [ [http://scienceworld.wolfram.com/physics/Pomega.html Pomega - from Eric Weisstein's World of Physics ] ]
* Comoving distance in cosmology. [ [http://odin.physastro.mnsu.edu/~eskridge/astr225/week14.html Outline for Weeks 14&15, Astronomy 225 Spring 2008 ] ]

In HTML, the capital letter Π can be produced using the codes Π or Π, and the lower-case by using π or π within the source code.

See also

*П, п - Pe (Cyrillic)
*Р, р - Er (Cyrillic)
*P, p - Pe (Latin)

References