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. Letters that arose from pi include Cyrillic Pe (П, п).

In Modern Greek, the name of the letter is Template:PronEng; in modern English, it is pronounced /paɪ/, in particular when referring to the mathematical constant (see below). In Greek the letter is pronounced /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.
• Comoving distance in cosmology.

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)