Pi (letter): Difference between revisions
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*{{unichar|03C0|GREEK SMALL LETTER PI|html=}} |
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*{{unichar|03D6|GREEK PI SYMBOL|html=}} |
*{{unichar|03D6|GREEK PI SYMBOL|html=}} |
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*{{unichar|220F|N-ARY PRODUCT|html=}} |
*{{unichar|220F|N-ARY PRODUCT|html=}} |
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*{{unichar|1D28|GREEK LETTER SMALL CAPITAL PI|html=}}<ref>[http://www.fileformat.info/info/unicode/font/calibri/list.htm Unicode characters supported by the Calibri font<!-- Bot generated title -->]</ref>. |
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==Character Encodings== |
==Character Encodings== |
Revision as of 01:46, 6 March 2013
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Pi (/[invalid input: 'icon']paɪ/; Greek: [pi], uppercase Π, lowercase π) is the sixteenth letter of the Greek alphabet, representing [p]. 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 Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).
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.
History
In the book 'L'alphabet grec' published at TheBookEdition, Thierry H. de Mortain explains that letter П is a gate, since first letter of ПYLH (gate of town or temple). The Greek wanted to represent the shape of the entrance to civilization; like the gate of the lions in Mycènes.
Variant pi
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:
- Angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by but this may be confused with vorticity in a fluid dynamics context).
- Longitude of pericenter, in celestial mechanics.[1]
- Comoving distance in cosmology.[2]
The various forms of pi are present in Unicode as:
- U+03A0 Π GREEK CAPITAL LETTER PI (Π)
- U+03C0 π GREEK SMALL LETTER PI (π)
- U+03D6 ϖ GREEK PI SYMBOL (ϖ, ϖ)
- U+220F ∏ N-ARY PRODUCT (∏, ∏)
- U+1D28 ᴨ GREEK LETTER SMALL CAPITAL PI[3].
Character Encodings
- Greek / Coptic Pi
Preview | Π | π | ϖ | Ⲡ | ⲡ | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL LETTER PI | GREEK SMALL LETTER PI | GREEK PI SYMBOL | COPTIC CAPITAL LETTER PI | COPTIC SMALL LETTER PI | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 928 | U+03A0 | 960 | U+03C0 | 982 | U+03D6 | 11424 | U+2CA0 | 11425 | U+2CA1 |
UTF-8 | 206 160 | CE A0 | 207 128 | CF 80 | 207 150 | CF 96 | 226 178 160 | E2 B2 A0 | 226 178 161 | E2 B2 A1 |
Numeric character reference | Π |
Π |
π |
π |
ϖ |
ϖ |
Ⲡ |
Ⲡ |
ⲡ |
ⲡ |
Named character reference | Π | π | ϖ, ϖ | |||||||
DOS Greek | 143 | 8F | 167 | A7 | ||||||
DOS Greek-2 | 198 | C6 | 234 | EA | ||||||
Windows 1253 | 208 | D0 | 240 | F0 | ||||||
TeX | \Pi | \pi | \varpi |
- Mathematical Pi
Preview | ∏ | ∐ | 𝚷 | 𝛑 | 𝛱 | 𝜋 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Unicode name | N-ARY PRODUCT | N-ARY COPRODUCT | MATHEMATICAL BOLD CAPITAL PI |
MATHEMATICAL BOLD SMALL PI |
MATHEMATICAL ITALIC CAPITAL PI |
MATHEMATICAL ITALIC SMALL PI | ||||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 8719 | U+220F | 8720 | U+2210 | 120503 | U+1D6B7 | 120529 | U+1D6D1 | 120561 | U+1D6F1 | 120587 | U+1D70B |
UTF-8 | 226 136 143 | E2 88 8F | 226 136 144 | E2 88 90 | 240 157 154 183 | F0 9D 9A B7 | 240 157 155 145 | F0 9D 9B 91 | 240 157 155 177 | F0 9D 9B B1 | 240 157 156 139 | F0 9D 9C 8B |
UTF-16 | 8719 | 220F | 8720 | 2210 | 55349 57015 | D835 DEB7 | 55349 57041 | D835 DED1 | 55349 57073 | D835 DEF1 | 55349 57099 | D835 DF0B |
Numeric character reference | ∏ |
∏ |
∐ |
∐ |
𝚷 |
𝚷 |
𝛑 |
𝛑 |
𝛱 |
𝛱 |
𝜋 |
𝜋 |
Named character reference | ∏, ∏ | ∐, ∐ |
Preview | 𝜫 | 𝝅 | 𝝥 | 𝝿 | 𝞟 | 𝞹 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL BOLD ITALIC CAPITAL PI |
MATHEMATICAL BOLD ITALIC SMALL PI |
MATHEMATICAL SANS-SERIF BOLD CAPITAL PI |
MATHEMATICAL SANS-SERIF BOLD SMALL PI |
MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PI |
MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PI | ||||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120619 | U+1D72B | 120645 | U+1D745 | 120677 | U+1D765 | 120703 | U+1D77F | 120735 | U+1D79F | 120761 | U+1D7B9 |
UTF-8 | 240 157 156 171 | F0 9D 9C AB | 240 157 157 133 | F0 9D 9D 85 | 240 157 157 165 | F0 9D 9D A5 | 240 157 157 191 | F0 9D 9D BF | 240 157 158 159 | F0 9D 9E 9F | 240 157 158 185 | F0 9D 9E B9 |
UTF-16 | 55349 57131 | D835 DF2B | 55349 57157 | D835 DF45 | 55349 57189 | D835 DF65 | 55349 57215 | D835 DF7F | 55349 57247 | D835 DF9F | 55349 57273 | D835 DFB9 |
Numeric character reference | 𝜫 |
𝜫 |
𝝅 |
𝝅 |
𝝥 |
𝝥 |
𝝿 |
𝝿 |
𝞟 |
𝞟 |
𝞹 |
𝞹 |
These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
See also
- П, п - Pe (Cyrillic)
- Р, р - Er (Cyrillic)
- P, p - Pe (Latin)
- Greek letters used in mathematics, science, and engineering#Ππ (pi)