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sigma

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**Sigma**(uppercase

**Î£**, lowercase

**Ïƒ**, lowercase in word-final position

**Ï‚**; ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. When used at the end of a word (when the word is not all caps), the final form (Ï‚) is used, e.g. (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end.

## History

The shape and alphabetic position of sigma is derived from Phoenician shinshin.### Etymology

The original name of the letter "sigma" may have been*san*, but due to the complicated early history of the Greek epichoric alphabets, "san" came to be identified as a separate letter, Ïº.ENCYCLOPEDIA, Encyclopedia of ancient Greece, Nigel Guy, Wilson, Alphabet, Roger D., Woodard, 2006, Routldedge, London, 38, Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians."" ('â€¦the same letter, which the Dorians call "san", but the Ionians "sigma"â€¦'; Herodotus,

*Histories*1.139); cf. Nick Nicholas,

*Non-Attic letters*{{webarchive|url=https://archive.is/20120628161421weblink |date=2012-06-28 }}.The name of sigma, according to one hypothesis,BOOK, Jeffery, Lilian H., The local scripts of archaic Greece, Oxford, Clarendon, 1961, 25â€“27, may continue that of Phoenician Samekh, the letter continued by Greek Îž.Alternatively, the name

*sigma*may have been a Greek innovation that simply meant "hissing", from the root of (

*{{transl|grc|sÃzÅ}}*, earlier *

*sig-jÅ*, meaning "I hiss").

### Lunate sigma

File:Madaba Jerusalem Mosaic.jpg -*Introduction to Greek and Latin paleography*, Oxford: Clarendon. p. 108, 144 It is also found on coins from the fourth century BC onward.Parthia.com:

*Numismatica Font Projects*. This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as

*lunate sigma*(uppercase Ï¹, lowercase Ï²), because of its crescent-like shape.It is still widely used in decorative typefaces in Greece, especially in religious and church contexts, as well as in some modern print editions of classical Greek texts. A dotted lunate sigma (

*sigma periestigmenon*, encoded at U+03FE Ï¾) was used by Aristarchus of Samothrace (220â€“143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an antisigma, or reversed sigma (Ï½), may mark a line that is out of place. A dotted antisigma or dotted reversed sigma (

*antisigma periestigmenon*: Ï¿) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.

### Derived alphabets

Sigma was adopted in the Old Italic alphabets beginning in the 8th century BC.A simplified three-stroke version, omitting the lowermost stroke, is found already in Western Greek alphabets, and becomes current in classical Etruscan, in Oscan, and also in the earliest Latin epigraphy (early Latin S), such as the Duenos inscription.The alternation between three and four strokes (occasionally also more than four) is also adopted into the early runic alphabet (early form of the*s*-rune.Both the Anglo-Saxon runes and the Younger Futhark consistently use the simplified three-stroke version. The forms of the Coptic letter {{coptic|â²¤}}

*sima*(2nd century BC) and of Cyrillic letter Ð¡ (9th century) are derived from lunate sigma.

## Uses

### Greek

In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative {{IPA|/s/}}. In Modern Greek, this sound is voiced to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/Ã°/}} or {{IPA|/É£/}}.### International African Alphabet

{{anchor|Uppercase of esh}}The uppercase form of sigma was re-borrowed into the Latin alphabet â€“ more precisely, the International African Alphabet â€“ to serve as the uppercase of modern esh (lowercase: Êƒ).### Science and mathematics

#### Uppercase

Uppercase Î£ is used as a symbol for:- the summation operator
- : e.g.: sum_{k=0}^5k= 0 + 1 + 2 + 3 + 4 + 5 = 15
- Sigma is the addition version of factorial.
- a class of baryons in particle physics
- macroscopic cross sections in nuclear and particle physics
- self-energy in condensed matter physics
- the balance of the invoice classes and the overall amount of the debts and demands in economics
- the set of symbols that form an alphabet in linguistics and computer science
- the covariance matrix of a set of random variables in probability theory and statistics, sometimes in the form ;|!!!Sigma to distinguish it from the summation operator.
- The busy beaver function

#### Lowercase

Lowercase Ïƒ is used for:- the standard deviation of a population or probability distribution in statistics
- sigma bonds in chemistry
- to represent an unknown angle in mathematics
- cross section (physics)
- velocity dispersion in astronomy
- sigma constant in organic chemistry
- the sigma receptor in biology
- a quality model for business, Six Sigma (6Ïƒ), based on the standard deviation
- sigma-algebras, sigma-fields, and sigma-finiteness in measure theory; in general terms, the symbol
*Ïƒ*serves as a shorthand for "countably", e.g. a*Ïƒ*-compact topological space is one that can be written as a countable union of compact subsets. - the generated sigma-algebra of a set
*A*is denoted*Ïƒ*(*A*) - the sum-of-divisors function in number theory
- the Stefanâ€“Boltzmann constant
- the "sigma factor" of RNA polymerase
- a measure of electrical conductivity
- the surface charge density in electrostatics
- normal stress in continuum mechanics
- volatility of a stock generally needed for options pricing
- a syllable in phonology
- the spectrum of a linear map
*T*, denoted as*Ïƒ*(*T*), in applied mathematics - surface tension
- the unary operation of selection on a database relation in relational algebra
- the Pauli matrices in quantum mechanics
- a target's radar cross-section (RCS) in radar jamming or electronic warfare
- the life span of a basic multicellular unit (BMU) in bone remodeling
- the damping parameter in signal processing
- a millisecond in early 20th-century physiology literatureJOURNAL, Hill, A. V., Units and Symbols, 10.1038/136222a0, Nature, 136, 3432, 222, 1935,
- the Weierstrass sigma-function
- the Sigmoid/Logistic function in machine learning
- the elasticity of substitution between two inputs in macroeconomics

### Organizations

{{anchor|Politics}}During the 1930s, an uppercase Î£ was in use as the symbol of the AÃ§Ã£o Integralista Brasileira, a fascist political party in Brazil.{{anchor|Companies}}Sigma Corporation uses the name of the letter but not the letter itself, but in many Internet forums, photographers refer to the company or its lenses using the letter. Sigma Aldrich incorporate both the name and the character in their logo.## Character encoding

- Greek Sigma

name1=Greek Capital Letter Sigma | name2=Greek Small Letter Sigma | name3=Greek Small Letter Final Sigma | name4=Greek Capital Lunate Sigma Symbol | name5=Greek Lunate Sigma Symbol | map2char1=91 | map2char3=AA | map3char1=CF | map3char3=ED | map4char1=D3 | map4char3=F2 | TeX>ref1char1=Sigma | ref1char3=varsigma}}Unicode Code Charts: Greek and Coptic (Range: 0370-03FF){{charmap | name1=Greek Capital Reversed Lunate Sigma Symbol | name2=Greek Small Reversed Lunate Sigma Symbol | name3=Greek Capital Dotted Lunate Sigma Symbol | name4=Greek Small Dotted Lunate Sigma Symbol | name5=Greek Capital Reversed Dotted Lunate Sigma Symbol | name6=Greek Small Reversed Dotted Lunate Sigma Symbol}}
- Coptic Sima
| name1=Coptic Capital Letter Sima | name2=Coptic Small Letter Sima}}
- Mathematical Sigma
| name1=N-ary Summation | name2=Mathematical BoldCapital Sigma | name3=Mathematical BoldSmall Sigma | name4=Mathematical BoldSmall Final Sigma | name5=Mathematical ItalicCapital Sigma | name6=Mathematical ItalicSmall Sigma}}{{charmap | name1=Mathematical ItalicSmall Final Sigma | name2=Mathematical Bold ItalicCapital Sigma | name3=Mathematical Bold ItalicSmall Sigma | name4=Mathematical Bold ItalicSmall Final Sigma | name5=Mathematical Sans-SerifBold Capital Sigma}}{{charmap | name1=Mathematical Sans-SerifBold Small Sigma | name2=Mathematical Sans-SerifBold Small Final Sigma | name3=Mathematical Sans-SerifBold Italic Capital Sigma | name4=Mathematical Sans-SerifBold Italic Small Sigma | name5=Mathematical Sans-SerifBold Italic Small Final Sigma}}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{{Wiktionary|Î£|Ïƒ|Ï‚}}- Antisigma
- Greek letters used in mathematics, science, and engineering
- Sampi
- Sho (letter)
- Stigma (letter)
- Sibilant consonant
- âˆ‘, or summation
- "Sigm-" as a combining form, as in
*sigm*odon,*sigm*urethra, or in the derivative "sigmoid", as in sigmoid sinus, sigmoid colon, sigmoidoscopy, etc.
## References{{Reflist}} |

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