Pi (uppercase Π, lower case π) is the sixteenth letter of the Greek alphabet, representing [p]. In the system of Greek numerals it has a value of 80. Letters that arose from pi include Cyrillic Pe(П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).
In Modern Greek, the name of the letter is pronounced [ˈpi]; in modern English, it is pronounced /ˈpaɪ/, in particular when referring to the mathematical constant (see below).
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 transcendental (and thusirrational) constant π ≈ 3.14159…, the ratio of acircle's circumference to its diameter inEuclidean 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.
- Homotopy groups in algebraic topology.
- 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.
- Economic profit in microeconomics.
- Inflation rate in macroeconomics.
- 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.
Variant pi or "pomega" (
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:
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:- perihelion
- The angular frequency of a wave in fluid dynamics (angular frequency is usually represented by ω but this may be confused with vorticity in a fluid dynamics context).
- The longitude of pericenter in celestial mechanics.[1]
- Comoving distance in cosmology.[2]
In Unicode, the code point for capital Π is U+03A0 and for lower-case π it is U+03C0. The code point for ϖ, called greek pi symbol, is U+03D6, and that for the product symbol ∏, called n-ary product, is U+220F.
