Pi
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| + | '''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 alphabet|Cyrillic]] [[Pe (Cyrillic)|Pe]] (П, п), [[Coptic alphabet|Coptic]] pi (Ⲡ, ⲡ), and [[Gothic alphabet|Gothic]] [[pairthra]] (𐍀). | ||
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| + | In Modern Greek, the name of the letter is pronounced ˈpi|; in modern English, it is ˈpaɪ, in particular when referring to the [[Pi|mathematical constant]] (see below). | ||
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| + | The upper-case letter Π is used as a symbol for: | ||
| + | * The [[product (mathematics)|product]] operator in mathematics, indicated with [[Multiplication#Capital Pi notation|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 [[Gospel]]s, 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 number|transcendental]] (and thus [[Irrational number|irrational]]) [[Pi|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. | ||
| + | * [[Homotopy group]]s 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 [[pion|pi meson or pion]]. | ||
| + | * [[Profit (economics)|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 (mathematics)|manifold]]. | ||
| + | * The unary operation of [[Projection (relational algebra)|projection]] in [[relational algebra]]. | ||
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| + | '''Variant pi''' or "pomega" (<math>\varpi\,\!</math> 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 [[ocean surface wave|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). | ||
| + | * The [[longitude of pericenter]] in [[celestial mechanics]].<sup>[]</sup> | ||
| + | * [[Comoving distance]] in cosmology.<sup>[]</sup> | ||
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| + | 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. | ||
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| + | In [[HTML]], the capital letter Π can be produced using the codes &Pi; or &#928;, and the lower-case by using &pi; or &#960; within the source code.<sup>[]</sup> | ||
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| + | == See also == | ||
| + | *[[Pe (Cyrillic)|П, п - Pe (Cyrillic)]] | ||
| + | *[[Er (Cyrillic)|Р, р - Er (Cyrillic)]] | ||
| + | *[[P|P, p - Pe (Latin)]] | ||
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| + | == References == | ||
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| + | [[Category:Greek letters]] | ||
Revision as of 23:47, 24 March 2011
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 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 thus 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.
- 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" (<math>\varpi\,\!</math> 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 <math>\omega</math> but this may be confused with vorticity in a fluid dynamics context).
- The longitude of pericenter in celestial mechanics.[]
- Comoving distance in cosmology.[]
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.
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.[]
