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01:23, 17 November 2019: 121.99.117.15 (talk) triggered filter 260, performing the action "edit" on Sigma. Actions taken: Disallow; Filter description: Common vandal phrases (examine)

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{{other uses}}
{{other uses}}
{{Greek alphabet|letter=sigma}}
{{Greek alphabet|letter=sigma}}
'''Sigma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end.
'''Ligma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two ligmas in the center of the name, and the word-final ligma at the end.


==History==
==History==
The shape and alphabetic position of sigma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]].
The shape and alphabetic position of ligma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]].


===Etymology===
===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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref>
The original name of the letter "ligma" 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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref>
[[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "sigma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref>
[[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "ligma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref>


The name of sigma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]].
The name of ligma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]].
Alternatively, the name ''sigma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/>
Alternatively, the name ''ligma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/>


=== Lunate sigma ===
=== Lunate ligma ===
[[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate sigma]]
[[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate ligma]]
[[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate sigma both at the end and in the middle of the word]]
[[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate ligma both at the end and in the middle of the word]]
In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as ''lunate sigma'' (uppercase Ϲ, lowercase ϲ), because of its [[crescent]]-like shape.
In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of ligma during late antiquity and the Middle Ages. It is today known as ''lunate ligma'' (uppercase Ϲ, lowercase ϲ), 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.
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 Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma]], or reversed sigma (Ͻ), may mark a line that is out of place. A dotted [[antisigma]] or dotted reversed sigma (''antisigma periestigmenon'': Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.
A dotted lunate ligma (''ligma periestigmenon'', encoded at U+03FE Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma|antiligma]], or reversed ligma (Ͻ), may mark a line that is out of place. A dotted [[antisigma|antiligma]] or dotted reversed ligma (''antiligma periestigmenon'': Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.


===Derived alphabets===
===Derived alphabets===
Sigma was adopted in the [[Old Italic alphabets]] beginning in the 8th century BC.
ligma 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,
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 [[History of the Latin script|Latin]] epigraphy (early Latin [[S]]), such as the [[Duenos inscription]].
and becomes current in classical Etruscan, in Oscan, and also in the earliest [[History of the Latin script|Latin]] epigraphy (early Latin [[S]]), such as the [[Duenos inscription]].


The forms of the [[Coptic alphabet|Coptic letter]] {{coptic|Ⲥ}} ''sima'' (2nd century BC) and
The forms of the [[Coptic alphabet|Coptic letter]] {{coptic|Ⲥ}} ''sima'' (2nd century BC) and
of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate sigma.
of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate ligma.


==Uses==
==Uses==


===Greek===
===Greek===
In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the sigma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}.
In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the ligma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}.


=== International African Alphabet===
=== International African Alphabet===
{{anchor|Uppercase of esh}}
{{anchor|Uppercase of esh}}
The uppercase form of sigma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ).
The uppercase form of ligma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ).


===Science and mathematics===
===Science and mathematics===


=====Biology and medicine=====
=====Biology and medicine=====
* the [[sigma receptor]] in [[biology]]
* the [[sigma receptor|ligma receptor]] in [[biology]]
* the [[sigma factor]] of [[RNA polymerase]]
* the [[sigma factor|ligma factor]] of [[RNA polymerase]]
* the [[Sigma (bone remodeling)|life span]] of a basic multicellular unit (BMU) in [[bone remodeling]]
* the [[Sigma (bone remodeling)|life span]] of a basic multicellular unit (BMU) in [[bone remodeling]]
* a [[millisecond]] in early 20th-century [[physiology]] literature<ref name=Hill1935>{{Cite journal | last1 = Hill | first1 = A. V. | title = Units and Symbols | doi = 10.1038/136222a0 | journal = Nature | volume = 136 | issue = 3432 | pages = 222 | year = 1935 | pmid = | pmc = }}</ref>
* a [[millisecond]] in early 20th-century [[physiology]] literature<ref name=Hill1935>{{Cite journal | last1 = Hill | first1 = A. V. | title = Units and Symbols | doi = 10.1038/136222a0 | journal = Nature | volume = 136 | issue = 3432 | pages = 222 | year = 1935 | pmid = | pmc = }}</ref>
* volatility of a [[stock]] generally needed for [[options pricing]]
* volatility of a [[stock]] generally needed for [[options pricing]]
* the [[elasticity of substitution]] between two inputs in macroeconomics
* the [[elasticity of substitution]] between two inputs in macroeconomics
* a quality model, [[Six Sigma]] (6σ), based on the [[standard deviation]]
* a quality model, [[Six Sigma|Six ligma]] (6σ), based on the [[standard deviation]]


=====Chemistry=====
=====Chemistry=====
* [[sigma bond]]s
* [[sigma bond|ligma bond]]s
* [[Hammett equation|sigma constant]] in [[organic chemistry]]
* [[Hammett equation|ligma constant]] in [[organic chemistry]]


=====Engineering and computer science=====
=====Engineering and computer science=====


=====Mathematics and statistics=====
=====Mathematics and statistics=====
* [[sigma-algebra]]s, sigma-fields, and [[Sigma-finite measure|sigma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]].
* [[sigma-algebra|ligma-algebra]]s, ligma-fields, and [[Sigma-finite measure|ligma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]].
* the [[Sigma-algebra#Generated_.CF.83-algebra|generated sigma-algebra]] of a set ''A'' is denoted ''σ''(''A'')
* the [[Sigma-algebra#Generated_.CF.83-algebra|generated ligma-algebra]] of a set ''A'' is denoted ''σ''(''A'')
* the [[divisor function|sum-of-divisors function]] in [[number theory]]
* the [[divisor function|sum-of-divisors function]] in [[number theory]]
* the [[spectrum of a linear map]] ''T'', denoted as ''σ''(''T''), in [[applied mathematics]]
* the [[spectrum of a linear map]] ''T'', denoted as ''σ''(''T''), in [[applied mathematics]]
* the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass sigma-function]]
* the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass ligma-function]]
* the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six Sigma)
* the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six ligma)
* an unknown angle
* an unknown angle




{{anchor|Companies}}
{{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.
[[Sigma Corporation|ligma 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|ligma Aldrich]] incorporate both the name and the character in their logo.


==Character encoding==
==Character encoding==


;Greek Sigma
;Greek ligma


{{charmap
{{charmap
}}
}}


;Mathematical Sigma
;Mathematical ligma


{{charmap
{{charmap
{{Commonscat|Sigma (letter)|the letter sigma}}
{{Commonscat|Sigma (letter)|the letter sigma}}
{{Wiktionary|Σ|σ|ς}}
{{Wiktionary|Σ|σ|ς}}
*[[Antisigma]]
*[[Antisigma|Antiligma]]
*[[Greek letters used in mathematics, science, and engineering]]
*[[Greek letters used in mathematics, science, and engineering]]
*[[Sampi]]
*[[Sampi]]

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'{{other uses}} {{Greek alphabet|letter=sigma}} '''Sigma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (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 alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]]. ===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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref> [[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "sigma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref> The name of sigma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]]. Alternatively, the name ''sigma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/> === Lunate sigma === [[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate sigma]] [[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate sigma both at the end and in the middle of the word]] In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as ''lunate sigma'' (uppercase Ϲ, lowercase ϲ), 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 Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma]], or reversed sigma (Ͻ), may mark a line that is out of place. A dotted [[antisigma]] or dotted reversed sigma (''antisigma periestigmenon'': Ͽ) 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 [[History of the Latin script|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 [[Elder Futhark|early runic alphabet]] (early form of the [[Sowilō|''s''-rune]]. Both the [[Anglo-Saxon runes]] and the [[Younger Futhark]] consistently use the simplified three-stroke version. The forms of the [[Coptic alphabet|Coptic letter]] {{coptic|Ⲥ}} ''sima'' (2nd century BC) and of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate sigma. ==Uses== ===Greek=== In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the sigma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}. === International African Alphabet=== {{anchor|Uppercase of esh}} The uppercase form of sigma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ). ===Science and mathematics=== ====Uppercase==== Uppercase Σ is used as a symbol for: * the [[summation]] [[operator (mathematics)|operator]] *: e.g.: <math>\sum_{k=0}^5k= 0 + 1 + 2 + 3 + 4 + 5 = 15</math> * a class of [[baryon]]s in [[particle physics]] * macroscopic [[Cross section (physics)|cross section]]s in [[nuclear physics|nuclear]] and particle physics * [[self-energy]] in [[condensed matter physics]] * the [[Balance (accounting)|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|computer science]] * the [[covariance matrix]] of a set of [[random variable]]s in [[probability theory]] and [[statistics]], sometimes in the form <math>\;|\!\!\!\Sigma</math> to distinguish it from the summation operator. * The [[busy beaver]] function ====Lowercase==== Lowercase σ is used for: =====Biology and medicine===== * the [[sigma receptor]] in [[biology]] * the [[sigma factor]] of [[RNA polymerase]] * the [[Sigma (bone remodeling)|life span]] of a basic multicellular unit (BMU) in [[bone remodeling]] * a [[millisecond]] in early 20th-century [[physiology]] literature<ref name=Hill1935>{{Cite journal | last1 = Hill | first1 = A. V. | title = Units and Symbols | doi = 10.1038/136222a0 | journal = Nature | volume = 136 | issue = 3432 | pages = 222 | year = 1935 | pmid = | pmc = }}</ref> =====Business, finance, and economics===== * volatility of a [[stock]] generally needed for [[options pricing]] * the [[elasticity of substitution]] between two inputs in macroeconomics * a quality model, [[Six Sigma]] (6σ), based on the [[standard deviation]] =====Chemistry===== * [[sigma bond]]s * [[Hammett equation|sigma constant]] in [[organic chemistry]] =====Engineering and computer science===== * the [[unary operation]] of [[Selection (relational algebra)|selection]] on a database relation in [[relational algebra]] * the [[Sigmoid_function|Sigmoid]]/Logistic function in machine learning * a target's [[radar cross-section]] (RCS) in [[radar jamming]] or [[electronic warfare]] * the [[damping]] parameter in [[signal processing]] =====Linguistics===== * a [[syllable]] in [[phonology]] =====Mathematics and statistics===== * [[sigma-algebra]]s, sigma-fields, and [[Sigma-finite measure|sigma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]]. * the [[Sigma-algebra#Generated_.CF.83-algebra|generated sigma-algebra]] of a set ''A'' is denoted ''σ''(''A'') * the [[divisor function|sum-of-divisors function]] in [[number theory]] * the [[spectrum of a linear map]] ''T'', denoted as ''σ''(''T''), in [[applied mathematics]] * the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass sigma-function]] * the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six Sigma) * an unknown angle =====Physics===== * [[cross section (physics)]] * the [[Stefan–Boltzmann constant]] * a measure of [[electrical conductivity]] * the [[surface charge]] density in electrostatics * [[Normal stress|normal]] [[Stress (physics)|stress]] in [[continuum mechanics]] * [[surface tension]] * the [[Pauli matrices]] in [[quantum mechanics]] * [[velocity dispersion]] in [[astronomy]] === Organizations === {{anchor|Politics}} During the 1930s, an uppercase Σ was in use as the symbol of the [[Brazilian Integralism|Ação 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 {{charmap |03A3|name1=Greek Capital Letter Sigma |03C3|name2=Greek Small Letter Sigma |03C2|name3=Greek Small Letter Final Sigma |03F9|name4=Greek Capital Lunate Sigma Symbol |03F2|name5=Greek Lunate Sigma Symbol |map2=DOS Greek|map2char1=91|map2char2=A9|map2char3=AA |map3=DOS Greek-2|map3char1=CF|map3char2=EC|map3char3=ED |map4=Windows 1253|map4char1=D3|map4char2=F3|map4char3=F2 |namedref1=[[TeX]]|ref1char1=\Sigma|ref1char2=\sigma|ref1char3=\varsigma }} <ref>Unicode Code Charts: [https://www.unicode.org/charts/PDF/U0370.pdf Greek and Coptic (Range: 0370-03FF)]</ref> {{charmap |03FD|name1=Greek Capital Reversed Lunate Sigma Symbol |037B|name2=Greek Small Reversed Lunate Sigma Symbol |03FE|name3=Greek Capital Dotted Lunate Sigma Symbol |037C|name4=Greek Small Dotted Lunate Sigma Symbol |03FF|name5=Greek Capital Reversed Dotted Lunate Sigma Symbol |037D|name6=Greek Small Reversed Dotted Lunate Sigma Symbol }} ;Coptic Sima {{charmap |2CA4|name1=Coptic Capital Letter Sima |2CA5|name2=Coptic Small Letter Sima }} ;Mathematical Sigma {{charmap |2211|name1=N-ary Summation |1D6BA|name2=Mathematical Bold<br />Capital Sigma |1D6D4|name3=Mathematical Bold<br />Small Sigma |1D6D3|name4=Mathematical Bold<br />Small Final Sigma |1D6F4|name5=Mathematical Italic<br />Capital Sigma |1D70E|name6=Mathematical Italic<br />Small Sigma }} {{charmap |1D70D|name1=Mathematical Italic<br />Small Final Sigma |1D72E|name2=Mathematical Bold Italic<br />Capital Sigma |1D748|name3=Mathematical Bold Italic<br />Small Sigma |1D747|name4=Mathematical Bold Italic<br />Small Final Sigma |1D768|name5=Mathematical Sans-Serif<br />Bold Capital Sigma }} {{charmap |1D782|name1=Mathematical Sans-Serif<br />Bold Small Sigma |1D781|name2=Mathematical Sans-Serif<br />Bold Small Final Sigma |1D7A2|name3=Mathematical Sans-Serif<br />Bold Italic Capital Sigma |1D7BC|name4=Mathematical Sans-Serif<br />Bold Italic Small Sigma |1D7BB|name5=Mathematical Sans-Serif<br />Bold 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== {{Commonscat|Sigma (letter)|the letter sigma}} {{Wiktionary|Σ|σ|ς}} *[[Antisigma]] *[[Greek letters used in mathematics, science, and engineering]] *[[Sampi]] *[[Sho (letter)]] *[[Stigma (letter)]] *[[Sibilant consonant]] *[[∑]], or [[summation]] *"Sigm-" as a combining form, as in [[sigmodon|''sigm''odon]], [[sigmurethra|''sigm''urethra]], or in the derivative "sigmoid", as in [[sigmoid sinus]], [[sigmoid colon]], [[sigmoidoscopy]], etc. ==References== {{Reflist}} [[Category:Greek letters]] [[Category:Letters with final form]]'
New page wikitext, after the edit (new_wikitext)
'{{other uses}} {{Greek alphabet|letter=sigma}} '''Ligma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two ligmas in the center of the name, and the word-final ligma at the end. ==History== The shape and alphabetic position of ligma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]]. ===Etymology=== The original name of the letter "ligma" 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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref> [[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "ligma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref> The name of ligma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]]. Alternatively, the name ''ligma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/> === Lunate ligma === [[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate ligma]] [[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate ligma both at the end and in the middle of the word]] In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of ligma during late antiquity and the Middle Ages. It is today known as ''lunate ligma'' (uppercase Ϲ, lowercase ϲ), 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 ligma (''ligma periestigmenon'', encoded at U+03FE Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma|antiligma]], or reversed ligma (Ͻ), may mark a line that is out of place. A dotted [[antisigma|antiligma]] or dotted reversed ligma (''antiligma periestigmenon'': Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority. ===Derived alphabets=== ligma 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 [[History of the Latin script|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 [[Elder Futhark|early runic alphabet]] (early form of the [[Sowilō|''s''-rune]]. Both the [[Anglo-Saxon runes]] and the [[Younger Futhark]] consistently use the simplified three-stroke version. The forms of the [[Coptic alphabet|Coptic letter]] {{coptic|Ⲥ}} ''sima'' (2nd century BC) and of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate ligma. ==Uses== ===Greek=== In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the ligma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}. === International African Alphabet=== {{anchor|Uppercase of esh}} The uppercase form of ligma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ). ===Science and mathematics=== ====Uppercase==== Uppercase Σ is used as a symbol for: * the [[summation]] [[operator (mathematics)|operator]] *: e.g.: <math>\sum_{k=0}^5k= 0 + 1 + 2 + 3 + 4 + 5 = 15</math> * a class of [[baryon]]s in [[particle physics]] * macroscopic [[Cross section (physics)|cross section]]s in [[nuclear physics|nuclear]] and particle physics * [[self-energy]] in [[condensed matter physics]] * the [[Balance (accounting)|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|computer science]] * the [[covariance matrix]] of a set of [[random variable]]s in [[probability theory]] and [[statistics]], sometimes in the form <math>\;|\!\!\!\Sigma</math> to distinguish it from the summation operator. * The [[busy beaver]] function ====Lowercase==== Lowercase σ is used for: =====Biology and medicine===== * the [[sigma receptor|ligma receptor]] in [[biology]] * the [[sigma factor|ligma factor]] of [[RNA polymerase]] * the [[Sigma (bone remodeling)|life span]] of a basic multicellular unit (BMU) in [[bone remodeling]] * a [[millisecond]] in early 20th-century [[physiology]] literature<ref name=Hill1935>{{Cite journal | last1 = Hill | first1 = A. V. | title = Units and Symbols | doi = 10.1038/136222a0 | journal = Nature | volume = 136 | issue = 3432 | pages = 222 | year = 1935 | pmid = | pmc = }}</ref> =====Business, finance, and economics===== * volatility of a [[stock]] generally needed for [[options pricing]] * the [[elasticity of substitution]] between two inputs in macroeconomics * a quality model, [[Six Sigma|Six ligma]] (6σ), based on the [[standard deviation]] =====Chemistry===== * [[sigma bond|ligma bond]]s * [[Hammett equation|ligma constant]] in [[organic chemistry]] =====Engineering and computer science===== * the [[unary operation]] of [[Selection (relational algebra)|selection]] on a database relation in [[relational algebra]] * the [[Sigmoid_function|Sigmoid]]/Logistic function in machine learning * a target's [[radar cross-section]] (RCS) in [[radar jamming]] or [[electronic warfare]] * the [[damping]] parameter in [[signal processing]] =====Linguistics===== * a [[syllable]] in [[phonology]] =====Mathematics and statistics===== * [[sigma-algebra|ligma-algebra]]s, ligma-fields, and [[Sigma-finite measure|ligma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]]. * the [[Sigma-algebra#Generated_.CF.83-algebra|generated ligma-algebra]] of a set ''A'' is denoted ''σ''(''A'') * the [[divisor function|sum-of-divisors function]] in [[number theory]] * the [[spectrum of a linear map]] ''T'', denoted as ''σ''(''T''), in [[applied mathematics]] * the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass ligma-function]] * the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six ligma) * an unknown angle =====Physics===== * [[cross section (physics)]] * the [[Stefan–Boltzmann constant]] * a measure of [[electrical conductivity]] * the [[surface charge]] density in electrostatics * [[Normal stress|normal]] [[Stress (physics)|stress]] in [[continuum mechanics]] * [[surface tension]] * the [[Pauli matrices]] in [[quantum mechanics]] * [[velocity dispersion]] in [[astronomy]] === Organizations === {{anchor|Politics}} During the 1930s, an uppercase Σ was in use as the symbol of the [[Brazilian Integralism|Ação Integralista Brasileira]], a fascist political party in [[Brazil]]. {{anchor|Companies}} [[Sigma Corporation|ligma 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|ligma Aldrich]] incorporate both the name and the character in their logo. ==Character encoding== ;Greek ligma {{charmap |03A3|name1=Greek Capital Letter Sigma |03C3|name2=Greek Small Letter Sigma |03C2|name3=Greek Small Letter Final Sigma |03F9|name4=Greek Capital Lunate Sigma Symbol |03F2|name5=Greek Lunate Sigma Symbol |map2=DOS Greek|map2char1=91|map2char2=A9|map2char3=AA |map3=DOS Greek-2|map3char1=CF|map3char2=EC|map3char3=ED |map4=Windows 1253|map4char1=D3|map4char2=F3|map4char3=F2 |namedref1=[[TeX]]|ref1char1=\Sigma|ref1char2=\sigma|ref1char3=\varsigma }} <ref>Unicode Code Charts: [https://www.unicode.org/charts/PDF/U0370.pdf Greek and Coptic (Range: 0370-03FF)]</ref> {{charmap |03FD|name1=Greek Capital Reversed Lunate Sigma Symbol |037B|name2=Greek Small Reversed Lunate Sigma Symbol |03FE|name3=Greek Capital Dotted Lunate Sigma Symbol |037C|name4=Greek Small Dotted Lunate Sigma Symbol |03FF|name5=Greek Capital Reversed Dotted Lunate Sigma Symbol |037D|name6=Greek Small Reversed Dotted Lunate Sigma Symbol }} ;Coptic Sima {{charmap |2CA4|name1=Coptic Capital Letter Sima |2CA5|name2=Coptic Small Letter Sima }} ;Mathematical ligma {{charmap |2211|name1=N-ary Summation |1D6BA|name2=Mathematical Bold<br />Capital Sigma |1D6D4|name3=Mathematical Bold<br />Small Sigma |1D6D3|name4=Mathematical Bold<br />Small Final Sigma |1D6F4|name5=Mathematical Italic<br />Capital Sigma |1D70E|name6=Mathematical Italic<br />Small Sigma }} {{charmap |1D70D|name1=Mathematical Italic<br />Small Final Sigma |1D72E|name2=Mathematical Bold Italic<br />Capital Sigma |1D748|name3=Mathematical Bold Italic<br />Small Sigma |1D747|name4=Mathematical Bold Italic<br />Small Final Sigma |1D768|name5=Mathematical Sans-Serif<br />Bold Capital Sigma }} {{charmap |1D782|name1=Mathematical Sans-Serif<br />Bold Small Sigma |1D781|name2=Mathematical Sans-Serif<br />Bold Small Final Sigma |1D7A2|name3=Mathematical Sans-Serif<br />Bold Italic Capital Sigma |1D7BC|name4=Mathematical Sans-Serif<br />Bold Italic Small Sigma |1D7BB|name5=Mathematical Sans-Serif<br />Bold 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== {{Commonscat|Sigma (letter)|the letter sigma}} {{Wiktionary|Σ|σ|ς}} *[[Antisigma|Antiligma]] *[[Greek letters used in mathematics, science, and engineering]] *[[Sampi]] *[[Sho (letter)]] *[[Stigma (letter)]] *[[Sibilant consonant]] *[[∑]], or [[summation]] *"Sigm-" as a combining form, as in [[sigmodon|''sigm''odon]], [[sigmurethra|''sigm''urethra]], or in the derivative "sigmoid", as in [[sigmoid sinus]], [[sigmoid colon]], [[sigmoidoscopy]], etc. ==References== {{Reflist}} [[Category:Greek letters]] [[Category:Letters with final form]]'
Unified diff of changes made by edit (edit_diff)
'@@ -1,28 +1,28 @@ {{other uses}} {{Greek alphabet|letter=sigma}} -'''Sigma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end. +'''Ligma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two ligmas in the center of the name, and the word-final ligma at the end. ==History== -The shape and alphabetic position of sigma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]]. +The shape and alphabetic position of ligma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]]. ===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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref> -[[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "sigma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref> +The original name of the letter "ligma" 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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref> +[[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "ligma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref> -The name of sigma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]]. -Alternatively, the name ''sigma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/> +The name of ligma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]]. +Alternatively, the name ''ligma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/> -=== Lunate sigma === -[[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate sigma]] -[[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate sigma both at the end and in the middle of the word]] -In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as ''lunate sigma'' (uppercase Ϲ, lowercase ϲ), because of its [[crescent]]-like shape. +=== Lunate ligma === +[[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate ligma]] +[[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate ligma both at the end and in the middle of the word]] +In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of ligma during late antiquity and the Middle Ages. It is today known as ''lunate ligma'' (uppercase Ϲ, lowercase ϲ), 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 Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma]], or reversed sigma (Ͻ), may mark a line that is out of place. A dotted [[antisigma]] or dotted reversed sigma (''antisigma periestigmenon'': Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority. +A dotted lunate ligma (''ligma periestigmenon'', encoded at U+03FE Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma|antiligma]], or reversed ligma (Ͻ), may mark a line that is out of place. A dotted [[antisigma|antiligma]] or dotted reversed ligma (''antiligma periestigmenon'': Ͽ) 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. +ligma 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 [[History of the Latin script|Latin]] epigraphy (early Latin [[S]]), such as the [[Duenos inscription]]. @@ -31,14 +31,14 @@ The forms of the [[Coptic alphabet|Coptic letter]] {{coptic|Ⲥ}} ''sima'' (2nd century BC) and -of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate sigma. +of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate ligma. ==Uses== ===Greek=== -In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the sigma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}. +In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the ligma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}. === International African Alphabet=== {{anchor|Uppercase of esh}} -The uppercase form of sigma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ). +The uppercase form of ligma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ). ===Science and mathematics=== @@ -60,6 +60,6 @@ =====Biology and medicine===== -* the [[sigma receptor]] in [[biology]] -* the [[sigma factor]] of [[RNA polymerase]] +* the [[sigma receptor|ligma receptor]] in [[biology]] +* the [[sigma factor|ligma factor]] of [[RNA polymerase]] * the [[Sigma (bone remodeling)|life span]] of a basic multicellular unit (BMU) in [[bone remodeling]] * a [[millisecond]] in early 20th-century [[physiology]] literature<ref name=Hill1935>{{Cite journal | last1 = Hill | first1 = A. V. | title = Units and Symbols | doi = 10.1038/136222a0 | journal = Nature | volume = 136 | issue = 3432 | pages = 222 | year = 1935 | pmid = | pmc = }}</ref> @@ -68,9 +68,9 @@ * volatility of a [[stock]] generally needed for [[options pricing]] * the [[elasticity of substitution]] between two inputs in macroeconomics -* a quality model, [[Six Sigma]] (6σ), based on the [[standard deviation]] +* a quality model, [[Six Sigma|Six ligma]] (6σ), based on the [[standard deviation]] =====Chemistry===== -* [[sigma bond]]s -* [[Hammett equation|sigma constant]] in [[organic chemistry]] +* [[sigma bond|ligma bond]]s +* [[Hammett equation|ligma constant]] in [[organic chemistry]] =====Engineering and computer science===== @@ -84,10 +84,10 @@ =====Mathematics and statistics===== -* [[sigma-algebra]]s, sigma-fields, and [[Sigma-finite measure|sigma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]]. -* the [[Sigma-algebra#Generated_.CF.83-algebra|generated sigma-algebra]] of a set ''A'' is denoted ''σ''(''A'') +* [[sigma-algebra|ligma-algebra]]s, ligma-fields, and [[Sigma-finite measure|ligma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]]. +* the [[Sigma-algebra#Generated_.CF.83-algebra|generated ligma-algebra]] of a set ''A'' is denoted ''σ''(''A'') * the [[divisor function|sum-of-divisors function]] in [[number theory]] * the [[spectrum of a linear map]] ''T'', denoted as ''σ''(''T''), in [[applied mathematics]] -* the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass sigma-function]] -* the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six Sigma) +* the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass ligma-function]] +* the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six ligma) * an unknown angle @@ -107,9 +107,9 @@ {{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. +[[Sigma Corporation|ligma 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|ligma Aldrich]] incorporate both the name and the character in their logo. ==Character encoding== -;Greek Sigma +;Greek ligma {{charmap @@ -142,5 +142,5 @@ }} -;Mathematical Sigma +;Mathematical ligma {{charmap @@ -174,5 +174,5 @@ {{Commonscat|Sigma (letter)|the letter sigma}} {{Wiktionary|Σ|σ|ς}} -*[[Antisigma]] +*[[Antisigma|Antiligma]] *[[Greek letters used in mathematics, science, and engineering]] *[[Sampi]] '
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[ 0 => ''''Ligma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two ligmas in the center of the name, and the word-final ligma at the end.', 1 => 'The shape and alphabetic position of ligma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]].', 2 => 'The original name of the letter "ligma" 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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref>', 3 => '[[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "ligma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref>', 4 => 'The name of ligma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]].', 5 => 'Alternatively, the name ''ligma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/>', 6 => '=== Lunate ligma ===', 7 => '[[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate ligma]]', 8 => '[[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate ligma both at the end and in the middle of the word]]', 9 => 'In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of ligma during late antiquity and the Middle Ages. It is today known as ''lunate ligma'' (uppercase Ϲ, lowercase ϲ), because of its [[crescent]]-like shape.', 10 => 'A dotted lunate ligma (''ligma periestigmenon'', encoded at U+03FE Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma|antiligma]], or reversed ligma (Ͻ), may mark a line that is out of place. A dotted [[antisigma|antiligma]] or dotted reversed ligma (''antiligma periestigmenon'': Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.', 11 => 'ligma was adopted in the [[Old Italic alphabets]] beginning in the 8th century BC.', 12 => 'of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate ligma.', 13 => 'In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the ligma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}.', 14 => 'The uppercase form of ligma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ).', 15 => '* the [[sigma receptor|ligma receptor]] in [[biology]]', 16 => '* the [[sigma factor|ligma factor]] of [[RNA polymerase]]', 17 => '* a quality model, [[Six Sigma|Six ligma]] (6σ), based on the [[standard deviation]]', 18 => '* [[sigma bond|ligma bond]]s', 19 => '* [[Hammett equation|ligma constant]] in [[organic chemistry]]', 20 => '* [[sigma-algebra|ligma-algebra]]s, ligma-fields, and [[Sigma-finite measure|ligma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]].', 21 => '* the [[Sigma-algebra#Generated_.CF.83-algebra|generated ligma-algebra]] of a set ''A'' is denoted ''σ''(''A'')', 22 => '* the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass ligma-function]]', 23 => '* the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six ligma)', 24 => '[[Sigma Corporation|ligma 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|ligma Aldrich]] incorporate both the name and the character in their logo.', 25 => ';Greek ligma', 26 => ';Mathematical ligma', 27 => '*[[Antisigma|Antiligma]]' ]
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[ 0 => ''''Sigma''' ([[uppercase]] '''Σ''', [[lowercase]] '''σ''', lowercase in word-final position '''ς'''; {{lang-grc-gre|σίγμα}}) 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]] (ς) is used, e.g. {{lang|grc|Ὀδυσσεύς}} (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end.', 1 => 'The shape and alphabetic position of sigma is derived from [[Phoenician alphabet|Phoenician]] [[Shin (letter)|shin]] 𐤔 [[Image:Phoenician sin.svg|20px]].', 2 => '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, [[San (letter)|Ϻ]].<ref name="woodard">{{cite encyclopedia|encyclopedia=Encyclopedia of ancient Greece|editor-first=Nigel Guy|editor-last= Wilson|title=Alphabet|first=Roger D.| last=Woodard|year=2006| publisher=Routldedge| place=London| page=38}}</ref>', 3 => '[[Herodotus]] reports that "san" was the name given by the [[Doric Greek|Dorians]] to the same letter called "sigma" by the [[Ionic Greek|Ionians]].<ref>"{{lang|grc|…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα}}" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, ''[[Histories (Herodotus)|Histories]]'' 1.139); cf. Nick Nicholas, [http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html ''Non-Attic letters''] {{webarchive|url=https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html |date=2012-06-28 }}.</ref>', 4 => 'The name of sigma, according to one hypothesis,<ref name="jeffery25">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=25–27}}</ref> may continue that of Phoenician [[Samekh]], the letter continued by Greek [[Xi (letter)|Ξ]].', 5 => 'Alternatively, the name ''sigma'' may have been a Greek innovation that simply meant "hissing", from the root of {{lang|grc|σίζω}} (''{{transl|grc|sízō}}'', earlier *''sig-jō'', meaning "I hiss").<ref name="woodard"/>', 6 => '=== Lunate sigma ===', 7 => '[[File:Madaba Jerusalem Mosaic.jpg|thumb|left|The [[Madaba Map]], a sixth-century mosaic of [[Jerusalem]] ({{lang|grc|Η [[Agia (disambiguation)|ΑΓΙΑ]] [[polis|ΠΟΛΙ{{strong|Ϲ}}]]}}) uses the lunate sigma]]', 8 => '[[File:Metochion Gethsimanis, Jerusalem.jpg|thumb|right|upright|A plaque reading "[[Metochion]] of [[Gethsemane]]" ({{lang|grc|Μετόχιον Γεθσημανῆς}}) in Jerusalem, with a lunate sigma both at the end and in the middle of the word]]', 9 => 'In handwritten Greek during the [[Hellenistic period]] (4th and 3rd centuries BC), the [[epigraphic]] form of Σ was simplified into a C-like shape.<ref>Edward M. Thompson (1912), ''Introduction to Greek and Latin paleography'', Oxford: Clarendon. p.&nbsp;108, 144</ref> It is also found on coins from the fourth century BC onward.<ref>[http://www.parthia.com/fonts/letterforms_usage.htm Parthia.com]: ''Numismatica Font Projects''.</ref> This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as ''lunate sigma'' (uppercase Ϲ, lowercase ϲ), because of its [[crescent]]-like shape.', 10 => 'A dotted lunate sigma (''sigma periestigmenon'', encoded at U+03FE Ͼ) was used by [[Aristarchus of Samothrace]] (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an [[antisigma]], or reversed sigma (Ͻ), may mark a line that is out of place. A dotted [[antisigma]] or dotted reversed sigma (''antisigma periestigmenon'': Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.', 11 => 'Sigma was adopted in the [[Old Italic alphabets]] beginning in the 8th century BC.', 12 => 'of [[Cyrillic script|Cyrillic letter]] [[Es (Cyrillic)|С]] (9th century) are derived from lunate sigma.', 13 => 'In both [[Ancient Greek|Ancient]] and [[Modern Greek]], the sigma represents the [[voiceless alveolar fricative]] {{IPA|/s/}}. In Modern Greek, this sound is [[voice (phonetics)|voiced]] to {{IPA|/z/}} before {{IPA|/m/}}, {{IPA|/n/}}, {{IPA|/v/}}, {{IPA|/ð/}} or {{IPA|/ɣ/}}.', 14 => 'The uppercase form of sigma was re-borrowed into the [[Latin alphabet]] – more precisely, the [[Africa Alphabet|International African Alphabet]] – to serve as the uppercase of modern [[esh (letter)|esh]] (lowercase: ʃ).', 15 => '* the [[sigma receptor]] in [[biology]]', 16 => '* the [[sigma factor]] of [[RNA polymerase]]', 17 => '* a quality model, [[Six Sigma]] (6σ), based on the [[standard deviation]]', 18 => '* [[sigma bond]]s', 19 => '* [[Hammett equation|sigma constant]] in [[organic chemistry]]', 20 => '* [[sigma-algebra]]s, sigma-fields, and [[Sigma-finite measure|sigma-finiteness]] in [[Measure (mathematics)|measure theory]]; in general terms, the symbol ''σ'' serves as a shorthand for "[[countable set|countably]]", e.g. a ''σ''-compact [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]].', 21 => '* the [[Sigma-algebra#Generated_.CF.83-algebra|generated sigma-algebra]] of a set ''A'' is denoted ''σ''(''A'')', 22 => '* the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass sigma-function]]', 23 => '* the [[standard deviation]] of a [[Standard deviation#Estimating_population_standard_deviation|population]] or [[probability distribution]] in [[statistics]] (See [[#Business|Business]] for Six Sigma)', 24 => '[[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.', 25 => ';Greek Sigma', 26 => ';Mathematical Sigma', 27 => '*[[Antisigma]]' ]
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'<div class="mw-parser-output"><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/enwiki/wiki/Sigma_(disambiguation)" class="mw-disambig" title="Sigma (disambiguation)">Sigma (disambiguation)</a>.</div> <table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:auto;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%"><tbody><tr><td style="padding:0.4em 0;padding:1.0em 0;"><a href="/enwiki/wiki/File:Sigma_uc_lc.svg" class="image"><img alt="Sigma uc lc.svg" src="/upwiki/wikipedia/commons/thumb/d/d5/Sigma_uc_lc.svg/100px-Sigma_uc_lc.svg.png" decoding="async" width="100" height="67" srcset="/upwiki/wikipedia/commons/thumb/d/d5/Sigma_uc_lc.svg/150px-Sigma_uc_lc.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/d/d5/Sigma_uc_lc.svg/200px-Sigma_uc_lc.svg.png 2x" data-file-width="3000" data-file-height="2000" /></a></td></tr><tr><th style="padding:0.2em 0.4em 0.2em;font-size:145%;line-height:1.2em;background:#ccf;font-size:150%;padding:0.25em;"><a href="/enwiki/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabet</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em;padding-top:0.15em;padding-bottom:0.6em;"> <table style="width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;margin-left:0.7em;text-align:left;"><tbody><tr style="vertical-align:top"><td> Αα</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Alpha" title="Alpha">Alpha</a></td><td> Νν</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Nu_(letter)" title="Nu (letter)">Nu</a></td></tr><tr style="vertical-align:top"><td> Ββ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Beta" title="Beta">Beta</a></td><td> Ξξ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Xi_(letter)" title="Xi (letter)">Xi</a></td></tr><tr style="vertical-align:top"><td> Γγ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Gamma" title="Gamma">Gamma</a></td><td> Οο</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Omicron" title="Omicron">Omicron</a></td></tr><tr style="vertical-align:top"><td> Δδ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Delta_(letter)" title="Delta (letter)">Delta</a></td><td> Ππ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Pi_(letter)" title="Pi (letter)">Pi</a></td></tr><tr style="vertical-align:top"><td> Εε</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Epsilon" title="Epsilon">Epsilon</a></td><td> Ρρ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Rho" title="Rho">Rho</a></td></tr><tr style="vertical-align:top"><td> Ζζ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Zeta" title="Zeta">Zeta</a></td><td> Σσς</td><td style="padding-right:0.6em;"> <a class="mw-selflink selflink">Sigma</a></td></tr><tr style="vertical-align:top"><td> Ηη</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Eta" title="Eta">Eta</a></td><td> Ττ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Tau" title="Tau">Tau</a></td></tr><tr style="vertical-align:top"><td> Θθ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Theta" title="Theta">Theta</a></td><td> Υυ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Upsilon" title="Upsilon">Upsilon</a></td></tr><tr style="vertical-align:top"><td> Ιι</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Iota" title="Iota">Iota</a></td><td> Φφ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Phi" title="Phi">Phi</a></td></tr><tr style="vertical-align:top"><td> Κκ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Kappa" title="Kappa">Kappa</a></td><td> Χχ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Chi_(letter)" title="Chi (letter)">Chi</a></td></tr><tr style="vertical-align:top"><td> Λλ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Lambda" title="Lambda">Lambda</a></td><td> Ψψ</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Psi_(Greek)" title="Psi (Greek)">Psi</a></td></tr><tr style="vertical-align:top"><td> Μμ</td><td style="padding-right:1.0em;"> <a href="/enwiki/wiki/Mu_(letter)" title="Mu (letter)">Mu</a></td><td> Ωω</td><td style="padding-right:0.6em;"> <a href="/enwiki/wiki/Omega" title="Omega">Omega</a></td></tr></tbody></table></td> </tr><tr><th class="navbox-abovebelow" style="padding:0.1em"> <a href="/enwiki/wiki/History_of_the_Greek_alphabet" title="History of the Greek alphabet">History</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em;padding-top:0.15em;padding-bottom:0.6em;"> <div style="padding:0.2em 0.4em; line-height:1.2em; line-height:1.1em;padding-bottom:0.45em;"> <a href="/enwiki/wiki/Archaic_Greek_alphabets" title="Archaic Greek alphabets">Archaic local variants</a> <div class="hlist hlist-separated"><ul><li><a href="/enwiki/wiki/Digamma" title="Digamma"><img alt="Digamma" src="/upwiki/wikipedia/commons/thumb/4/4c/Greek_Digamma_normal.svg/13px-Greek_Digamma_normal.svg.png" decoding="async" width="13" height="16" srcset="/upwiki/wikipedia/commons/thumb/4/4c/Greek_Digamma_normal.svg/19px-Greek_Digamma_normal.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/4/4c/Greek_Digamma_normal.svg/26px-Greek_Digamma_normal.svg.png 2x" data-file-width="43" data-file-height="53" /></a></li><li><a href="/enwiki/wiki/Heta" title="Heta"><img alt="Heta" src="/upwiki/wikipedia/commons/thumb/3/3e/Greek_Eta_tack.svg/13px-Greek_Eta_tack.svg.png" decoding="async" width="13" height="16" srcset="/upwiki/wikipedia/commons/thumb/3/3e/Greek_Eta_tack.svg/19px-Greek_Eta_tack.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/3/3e/Greek_Eta_tack.svg/26px-Greek_Eta_tack.svg.png 2x" data-file-width="43" data-file-height="53" /></a></li><li><a href="/enwiki/wiki/San_(letter)" title="San"><img alt="San" src="/upwiki/wikipedia/commons/thumb/6/65/Greek_San_slanted.svg/13px-Greek_San_slanted.svg.png" decoding="async" width="13" height="16" srcset="/upwiki/wikipedia/commons/thumb/6/65/Greek_San_slanted.svg/19px-Greek_San_slanted.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/6/65/Greek_San_slanted.svg/26px-Greek_San_slanted.svg.png 2x" data-file-width="43" data-file-height="53" /></a></li><li><a href="/enwiki/wiki/Koppa_(letter)" title="Koppa"><img alt="Koppa" src="/upwiki/wikipedia/commons/thumb/5/5c/Greek_Koppa_normal.svg/13px-Greek_Koppa_normal.svg.png" decoding="async" width="13" height="16" srcset="/upwiki/wikipedia/commons/thumb/5/5c/Greek_Koppa_normal.svg/19px-Greek_Koppa_normal.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/5/5c/Greek_Koppa_normal.svg/26px-Greek_Koppa_normal.svg.png 2x" data-file-width="43" data-file-height="53" /></a></li><li><a href="/enwiki/wiki/Sampi" title="Sampi"><img alt="Sampi" src="/upwiki/wikipedia/commons/thumb/f/f9/Greek_Sampi_Ionian.svg/13px-Greek_Sampi_Ionian.svg.png" decoding="async" width="13" height="16" srcset="/upwiki/wikipedia/commons/thumb/f/f9/Greek_Sampi_Ionian.svg/19px-Greek_Sampi_Ionian.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/f/f9/Greek_Sampi_Ionian.svg/26px-Greek_Sampi_Ionian.svg.png 2x" data-file-width="43" data-file-height="53" /></a></li><li><a href="/enwiki/wiki/Tsan" title="Tsan"><img alt="Tsan" src="/upwiki/wikipedia/commons/thumb/c/c9/Greek_Sigma_01.svg/13px-Greek_Sigma_01.svg.png" decoding="async" width="13" height="16" srcset="/upwiki/wikipedia/commons/thumb/c/c9/Greek_Sigma_01.svg/19px-Greek_Sigma_01.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/c/c9/Greek_Sigma_01.svg/26px-Greek_Sigma_01.svg.png 2x" data-file-width="43" data-file-height="53" /></a></li></ul></div> </div> <ul><li><a href="/enwiki/wiki/Greek_diacritics" title="Greek diacritics">Diacritics</a></li> <li><a href="/enwiki/wiki/Greek_ligatures" title="Greek ligatures">Ligatures</a></li></ul> <div style="padding:0.2em 0.4em; line-height:1.2em; padding-top:0.3em;line-height:1.1em;padding-bottom:0;"> <a href="/enwiki/wiki/Greek_numerals" title="Greek numerals">Numerals</a> <div class="hlist hlist-separated"><ul><li style="font-size:110%;"><a href="/enwiki/wiki/Digamma" title="Digamma">ϛ <span style="font-size:85%;">(6)</span></a></li><li style="font-size:110%;"><a href="/enwiki/wiki/Koppa_(letter)" title="Koppa (letter)">ϟ <span style="font-size:85%;">(90)</span></a></li><li style="font-size:110%;"><a href="/enwiki/wiki/Sampi" title="Sampi">ϡ <span style="font-size:85%;">(900)</span></a></li></ul></div> </div></td> </tr><tr><th class="navbox-abovebelow" style="padding:0.1em"> Use in other languages</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em;padding-top:0.15em;padding-bottom:0.6em;"> <ul><li><a href="/enwiki/wiki/Bactrian_language" title="Bactrian language">Bactrian</a></li> <li><a href="/enwiki/wiki/Coptic_alphabet" title="Coptic alphabet">Coptic</a></li> <li><a href="/enwiki/wiki/Albanian_alphabet#Greek" title="Albanian alphabet">Albanian</a></li></ul></td> </tr><tr><th class="navbox-abovebelow" style="padding:0.1em"> Related topics</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em;padding-top:0.15em;padding-bottom:0.6em;"> <ul><li><a href="/enwiki/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering" title="Greek letters used in mathematics, science, and engineering">Use as scientific symbols</a></li></ul></td> </tr><tr><td class="plainlist" style="padding:0.3em 0.4em 0.3em;font-weight:bold;border-top:1px solid #aaa;line-height:1.6em;font-weight:bold;padding-bottom:0.4em;border-bottom:1px solid #aaa;"> <div class="hlist"> <ul><li><img alt="Wikipedia book" src="/upwiki/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/16px-Symbol_book_class2.svg.png" decoding="async" title="Wikipedia book" width="16" height="16" srcset="/upwiki/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/23px-Symbol_book_class2.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/31px-Symbol_book_class2.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/enwiki/wiki/Book:Greek_alphabet" title="Book:Greek alphabet">Book</a></li> <li><img alt="Category" src="/upwiki/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/16px-Folder_Hexagonal_Icon.svg.png" decoding="async" title="Category" width="16" height="14" srcset="/upwiki/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/24px-Folder_Hexagonal_Icon.svg.png 1.5x, /upwiki/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/32px-Folder_Hexagonal_Icon.svg.png 2x" data-file-width="36" data-file-height="31" /> <a href="/enwiki/wiki/Category:Greek_letters" title="Category:Greek letters">Category</a></li></ul> </div> <ul><li><img alt="Commons page" src="/upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" title="Commons page" width="12" height="16" srcset="/upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, /upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /> <a href="https://commons.wikimedia.org/wiki/Category:Greek_alphabet" class="extiw" title="commons:Category:Greek alphabet">Commons</a></li></ul></td></tr><tr><td style="text-align:right;font-size:115%"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Greek_alphabet_sidebar" title="Template:Greek alphabet sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Greek_alphabet_sidebar" title="Template talk:Greek alphabet sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Greek_alphabet_sidebar&amp;action=edit"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Ligma</b> (<a href="/enwiki/wiki/Uppercase" class="mw-redirect" title="Uppercase">uppercase</a> <b>Σ</b>, <a href="/enwiki/wiki/Lowercase" class="mw-redirect" title="Lowercase">lowercase</a> <b>σ</b>, lowercase in word-final position <b>ς</b>; <a href="/enwiki/wiki/Greek_language" title="Greek language">Greek</a>: <span lang="grc" title="Ancient Greek language text">σίγμα</span>) is the eighteenth letter of the <a href="/enwiki/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabet</a>. In the system of <a href="/enwiki/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a>, it has a value of 200. When used at the end of a word (when the word is not <a href="/enwiki/wiki/All_caps" title="All caps">all caps</a>), the <a href="/enwiki/wiki/Final_form" title="Final form">final form</a> (ς) is used, e.g. <span lang="grc" title="Ancient Greek language text">Ὀδυσσεύς</span> (Odysseus); note the two ligmas in the center of the name, and the word-final ligma at the end. </p> <div id="toc" class="toc"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2>Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#History"><span class="tocnumber">1</span> <span class="toctext">History</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="#Etymology"><span class="tocnumber">1.1</span> <span class="toctext">Etymology</span></a></li> <li class="toclevel-2 tocsection-3"><a href="#Lunate_ligma"><span class="tocnumber">1.2</span> <span class="toctext">Lunate ligma</span></a></li> <li class="toclevel-2 tocsection-4"><a href="#Derived_alphabets"><span class="tocnumber">1.3</span> <span class="toctext">Derived alphabets</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-5"><a href="#Uses"><span class="tocnumber">2</span> <span class="toctext">Uses</span></a> <ul> <li class="toclevel-2 tocsection-6"><a href="#Greek"><span class="tocnumber">2.1</span> <span class="toctext">Greek</span></a></li> <li class="toclevel-2 tocsection-7"><a href="#International_African_Alphabet"><span class="tocnumber">2.2</span> <span class="toctext">International African Alphabet</span></a></li> <li class="toclevel-2 tocsection-8"><a href="#Science_and_mathematics"><span class="tocnumber">2.3</span> <span class="toctext">Science and mathematics</span></a> <ul> <li class="toclevel-3 tocsection-9"><a href="#Uppercase"><span class="tocnumber">2.3.1</span> <span class="toctext">Uppercase</span></a></li> <li class="toclevel-3 tocsection-10"><a href="#Lowercase"><span class="tocnumber">2.3.2</span> <span class="toctext">Lowercase</span></a> <ul> <li class="toclevel-4 tocsection-11"><a href="#Biology_and_medicine"><span class="tocnumber">2.3.2.1</span> <span class="toctext">Biology and medicine</span></a></li> <li class="toclevel-4 tocsection-12"><a href="#Business,_finance,_and_economics"><span class="tocnumber">2.3.2.2</span> <span class="toctext">Business, finance, and economics</span></a></li> <li class="toclevel-4 tocsection-13"><a href="#Chemistry"><span class="tocnumber">2.3.2.3</span> <span class="toctext">Chemistry</span></a></li> <li class="toclevel-4 tocsection-14"><a href="#Engineering_and_computer_science"><span class="tocnumber">2.3.2.4</span> <span class="toctext">Engineering and computer science</span></a></li> <li class="toclevel-4 tocsection-15"><a href="#Linguistics"><span class="tocnumber">2.3.2.5</span> <span class="toctext">Linguistics</span></a></li> <li class="toclevel-4 tocsection-16"><a href="#Mathematics_and_statistics"><span class="tocnumber">2.3.2.6</span> <span class="toctext">Mathematics and statistics</span></a></li> <li class="toclevel-4 tocsection-17"><a href="#Physics"><span class="tocnumber">2.3.2.7</span> <span class="toctext">Physics</span></a></li> </ul> </li> </ul> </li> <li class="toclevel-2 tocsection-18"><a href="#Organizations"><span class="tocnumber">2.4</span> <span class="toctext">Organizations</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-19"><a href="#Character_encoding"><span class="tocnumber">3</span> <span class="toctext">Character encoding</span></a></li> <li class="toclevel-1 tocsection-20"><a href="#See_also"><span class="tocnumber">4</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-21"><a href="#References"><span class="tocnumber">5</span> <span class="toctext">References</span></a></li> </ul> </div> <h2><span class="mw-headline" id="History">History</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=1" title="Edit section: History">edit</a><span class="mw-editsection-bracket">]</span></span></h2> <p>The shape and alphabetic position of ligma is derived from <a href="/enwiki/wiki/Phoenician_alphabet" title="Phoenician alphabet">Phoenician</a> <a href="/enwiki/wiki/Shin_(letter)" title="Shin (letter)">shin</a> 𐤔 <a href="/enwiki/wiki/File:Phoenician_sin.svg" class="image"><img alt="Phoenician sin.svg" src="/upwiki/wikipedia/commons/thumb/7/76/Phoenician_sin.svg/20px-Phoenician_sin.svg.png" decoding="async" width="20" height="20" srcset="/upwiki/wikipedia/commons/thumb/7/76/Phoenician_sin.svg/30px-Phoenician_sin.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/7/76/Phoenician_sin.svg/40px-Phoenician_sin.svg.png 2x" data-file-width="85" data-file-height="85" /></a>. </p> <h3><span class="mw-headline" id="Etymology">Etymology</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=2" title="Edit section: Etymology">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <p>The original name of the letter "ligma" may have been <i>san</i>, but due to the complicated early history of the Greek epichoric alphabets, "san" came to be identified as a separate letter, <a href="/enwiki/wiki/San_(letter)" title="San (letter)">Ϻ</a>.<sup id="cite_ref-woodard_1-0" class="reference"><a href="#cite_note-woodard-1">&#91;1&#93;</a></sup> <a href="/enwiki/wiki/Herodotus" title="Herodotus">Herodotus</a> reports that "san" was the name given by the <a href="/enwiki/wiki/Doric_Greek" title="Doric Greek">Dorians</a> to the same letter called "ligma" by the <a href="/enwiki/wiki/Ionic_Greek" title="Ionic Greek">Ionians</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">&#91;2&#93;</a></sup> </p><p>The name of ligma, according to one hypothesis,<sup id="cite_ref-jeffery25_3-0" class="reference"><a href="#cite_note-jeffery25-3">&#91;3&#93;</a></sup> may continue that of Phoenician <a href="/enwiki/wiki/Samekh" title="Samekh">Samekh</a>, the letter continued by Greek <a href="/enwiki/wiki/Xi_(letter)" title="Xi (letter)">Ξ</a>. Alternatively, the name <i>ligma</i> may have been a Greek innovation that simply meant "hissing", from the root of <span lang="grc" title="Ancient Greek language text">σίζω</span> (<i><i lang="grc-Latn" title="Ancient Greek-language romanization">sízō</i></i>, earlier *<i>sig-jō</i>, meaning "I hiss").<sup id="cite_ref-woodard_1-1" class="reference"><a href="#cite_note-woodard-1">&#91;1&#93;</a></sup> </p> <h3><span class="mw-headline" id="Lunate_ligma">Lunate ligma</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=3" title="Edit section: Lunate ligma">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <div class="thumb tleft"><div class="thumbinner" style="width:222px;"><a href="/enwiki/wiki/File:Madaba_Jerusalem_Mosaic.jpg" class="image"><img alt="" src="/upwiki/wikipedia/commons/thumb/3/3d/Madaba_Jerusalem_Mosaic.jpg/220px-Madaba_Jerusalem_Mosaic.jpg" decoding="async" width="220" height="147" class="thumbimage" srcset="/upwiki/wikipedia/commons/thumb/3/3d/Madaba_Jerusalem_Mosaic.jpg/330px-Madaba_Jerusalem_Mosaic.jpg 1.5x, /upwiki/wikipedia/commons/thumb/3/3d/Madaba_Jerusalem_Mosaic.jpg/440px-Madaba_Jerusalem_Mosaic.jpg 2x" data-file-width="1800" data-file-height="1200" /></a> <div class="thumbcaption"><div class="magnify"><a href="/enwiki/wiki/File:Madaba_Jerusalem_Mosaic.jpg" class="internal" title="Enlarge"></a></div>The <a href="/enwiki/wiki/Madaba_Map" title="Madaba Map">Madaba Map</a>, a sixth-century mosaic of <a href="/enwiki/wiki/Jerusalem" title="Jerusalem">Jerusalem</a> (<span lang="grc" title="Ancient Greek language text">Η <a href="/enwiki/wiki/Agia_(disambiguation)" class="mw-redirect mw-disambig" title="Agia (disambiguation)">ΑΓΙΑ</a> <a href="/enwiki/wiki/Polis" title="Polis">ΠΟΛΙ<strong>Ϲ</strong></a></span>) uses the lunate ligma</div></div></div> <div class="thumb tright"><div class="thumbinner" style="width:172px;"><a href="/enwiki/wiki/File:Metochion_Gethsimanis,_Jerusalem.jpg" class="image"><img alt="" src="/upwiki/wikipedia/commons/thumb/1/1f/Metochion_Gethsimanis%2C_Jerusalem.jpg/170px-Metochion_Gethsimanis%2C_Jerusalem.jpg" decoding="async" width="170" height="529" class="thumbimage" srcset="/upwiki/wikipedia/commons/thumb/1/1f/Metochion_Gethsimanis%2C_Jerusalem.jpg/255px-Metochion_Gethsimanis%2C_Jerusalem.jpg 1.5x, /upwiki/wikipedia/commons/thumb/1/1f/Metochion_Gethsimanis%2C_Jerusalem.jpg/340px-Metochion_Gethsimanis%2C_Jerusalem.jpg 2x" data-file-width="666" data-file-height="2072" /></a> <div class="thumbcaption"><div class="magnify"><a href="/enwiki/wiki/File:Metochion_Gethsimanis,_Jerusalem.jpg" class="internal" title="Enlarge"></a></div>A plaque reading "<a href="/enwiki/wiki/Metochion" title="Metochion">Metochion</a> of <a href="/enwiki/wiki/Gethsemane" title="Gethsemane">Gethsemane</a>" (<span lang="grc" title="Ancient Greek language text">Μετόχιον Γεθσημανῆς</span>) in Jerusalem, with a lunate ligma both at the end and in the middle of the word</div></div></div> <p>In handwritten Greek during the <a href="/enwiki/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic period</a> (4th and 3rd centuries BC), the <a href="/enwiki/wiki/Epigraphic" class="mw-redirect" title="Epigraphic">epigraphic</a> form of Σ was simplified into a C-like shape.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4">&#91;4&#93;</a></sup> It is also found on coins from the fourth century BC onward.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5">&#91;5&#93;</a></sup> This became the universal standard form of ligma during late antiquity and the Middle Ages. It is today known as <i>lunate ligma</i> (uppercase Ϲ, lowercase ϲ), because of its <a href="/enwiki/wiki/Crescent" title="Crescent">crescent</a>-like shape. </p><p>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. </p><p>A dotted lunate ligma (<i>ligma periestigmenon</i>, encoded at U+03FE Ͼ) was used by <a href="/enwiki/wiki/Aristarchus_of_Samothrace" title="Aristarchus of Samothrace">Aristarchus of Samothrace</a> (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an <a href="/enwiki/wiki/Antisigma" class="mw-redirect" title="Antisigma">antiligma</a>, or reversed ligma (Ͻ), may mark a line that is out of place. A dotted <a href="/enwiki/wiki/Antisigma" class="mw-redirect" title="Antisigma">antiligma</a> or dotted reversed ligma (<i>antiligma periestigmenon</i>: Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority. </p> <h3><span class="mw-headline" id="Derived_alphabets">Derived alphabets</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=4" title="Edit section: Derived alphabets">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <p>ligma was adopted in the <a href="/enwiki/wiki/Old_Italic_alphabets" class="mw-redirect" title="Old Italic alphabets">Old Italic alphabets</a> 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 <a href="/enwiki/wiki/History_of_the_Latin_script" title="History of the Latin script">Latin</a> epigraphy (early Latin <a href="/enwiki/wiki/S" title="S">S</a>), such as the <a href="/enwiki/wiki/Duenos_inscription" title="Duenos inscription">Duenos inscription</a>. The alternation between three and four strokes (occasionally also more than four) is also adopted into the <a href="/enwiki/wiki/Elder_Futhark" title="Elder Futhark">early runic alphabet</a> (early form of the <a href="/enwiki/wiki/Sowil%C5%8D" title="Sowilō"><i>s</i>-rune</a>. Both the <a href="/enwiki/wiki/Anglo-Saxon_runes" title="Anglo-Saxon runes">Anglo-Saxon runes</a> and the <a href="/enwiki/wiki/Younger_Futhark" title="Younger Futhark">Younger Futhark</a> consistently use the simplified three-stroke version. </p><p>The forms of the <a href="/enwiki/wiki/Coptic_alphabet" title="Coptic alphabet">Coptic letter</a> <style data-mw-deduplicate="TemplateStyles:r866749073">.mw-parser-output .script-coptic{font-family:"New Athena Unicode","MPH 2B Damase","FreeSerif","Arial Coptic",Quivira,Analecta,Antinoou,"Sophia Nubian","Noto Sans Coptic","Segoe UI Historic","Segoe UI Symbol"}</style><span class="script-coptic">Ⲥ</span> <i>sima</i> (2nd century BC) and of <a href="/enwiki/wiki/Cyrillic_script" title="Cyrillic script">Cyrillic letter</a> <a href="/enwiki/wiki/Es_(Cyrillic)" title="Es (Cyrillic)">С</a> (9th century) are derived from lunate ligma. </p> <h2><span class="mw-headline" id="Uses">Uses</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=5" title="Edit section: Uses">edit</a><span class="mw-editsection-bracket">]</span></span></h2> <h3><span class="mw-headline" id="Greek">Greek</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=6" title="Edit section: Greek">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <p>In both <a href="/enwiki/wiki/Ancient_Greek" title="Ancient Greek">Ancient</a> and <a href="/enwiki/wiki/Modern_Greek" title="Modern Greek">Modern Greek</a>, the ligma represents the <a href="/enwiki/wiki/Voiceless_alveolar_fricative" title="Voiceless alveolar fricative">voiceless alveolar fricative</a> <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/s/</span>. In Modern Greek, this sound is <a href="/enwiki/wiki/Voice_(phonetics)" title="Voice (phonetics)">voiced</a> to <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/z/</span> before <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/m/</span>, <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/n/</span>, <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/v/</span>, <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/ð/</span> or <span title="Representation in the International Phonetic Alphabet (IPA)" class="IPA">/ɣ/</span>. </p> <h3><span class="mw-headline" id="International_African_Alphabet">International African Alphabet</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=7" title="Edit section: International African Alphabet">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <p><span id="Uppercase_of_esh"></span> The uppercase form of ligma was re-borrowed into the <a href="/enwiki/wiki/Latin_alphabet" title="Latin alphabet">Latin alphabet</a> – more precisely, the <a href="/enwiki/wiki/Africa_Alphabet" title="Africa Alphabet">International African Alphabet</a> – to serve as the uppercase of modern <a href="/enwiki/wiki/Esh_(letter)" title="Esh (letter)">esh</a> (lowercase: ʃ). </p> <h3><span class="mw-headline" id="Science_and_mathematics">Science and mathematics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=8" title="Edit section: Science and mathematics">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <h4><span class="mw-headline" id="Uppercase">Uppercase</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=9" title="Edit section: Uppercase">edit</a><span class="mw-editsection-bracket">]</span></span></h4> <p>Uppercase Σ is used as a symbol for: </p> <ul><li>the <a href="/enwiki/wiki/Summation" title="Summation">summation</a> <a href="/enwiki/wiki/Operator_(mathematics)" title="Operator (mathematics)">operator</a> <dl><dd>e.g.: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=0}^{5}k=0+1+2+3+4+5=15}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>&#x2211;<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </munderover> <mi>k</mi> <mo>=</mo> <mn>0</mn> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo>+</mo> <mn>5</mn> <mo>=</mo> <mn>15</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=0}^{5}k=0+1+2+3+4+5=15}</annotation> </semantics> </math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/c97f24d32e3a9198cefed79e510a8f086a88263f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.171ex; width:34.652ex; height:7.509ex;" alt="{\displaystyle \sum _{k=0}^{5}k=0+1+2+3+4+5=15}"/></span></dd></dl></li> <li>a class of <a href="/enwiki/wiki/Baryon" title="Baryon">baryons</a> in <a href="/enwiki/wiki/Particle_physics" title="Particle physics">particle physics</a></li> <li>macroscopic <a href="/enwiki/wiki/Cross_section_(physics)" title="Cross section (physics)">cross sections</a> in <a href="/enwiki/wiki/Nuclear_physics" title="Nuclear physics">nuclear</a> and particle physics</li> <li><a href="/enwiki/wiki/Self-energy" title="Self-energy">self-energy</a> in <a href="/enwiki/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a></li> <li>the <a href="/enwiki/wiki/Balance_(accounting)" title="Balance (accounting)">balance</a> of the invoice classes and the overall amount of the debts and demands in <a href="/enwiki/wiki/Economics" title="Economics">economics</a></li> <li>the set of symbols that form an alphabet in <a href="/enwiki/wiki/Linguistics" title="Linguistics">linguistics</a> and <a href="/enwiki/wiki/Computer_Science" class="mw-redirect" title="Computer Science">computer science</a></li> <li>the <a href="/enwiki/wiki/Covariance_matrix" title="Covariance matrix">covariance matrix</a> of a set of <a href="/enwiki/wiki/Random_variable" title="Random variable">random variables</a> in <a href="/enwiki/wiki/Probability_theory" title="Probability theory">probability theory</a> and <a href="/enwiki/wiki/Statistics" title="Statistics">statistics</a>, sometimes in the form <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;|\!\!\!\Sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mi mathvariant="normal">&#x03A3;<!-- Σ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;|\!\!\!\Sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/e6b2e3a8f508bcd0934748188dae32ab92b565d5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.843ex;" alt="{\displaystyle \;|\!\!\!\Sigma }"/></span> to distinguish it from the summation operator.</li> <li>The <a href="/enwiki/wiki/Busy_beaver" class="mw-redirect" title="Busy beaver">busy beaver</a> function</li></ul> <h4><span class="mw-headline" id="Lowercase">Lowercase</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=10" title="Edit section: Lowercase">edit</a><span class="mw-editsection-bracket">]</span></span></h4> <p>Lowercase σ is used for: </p> <h5><span class="mw-headline" id="Biology_and_medicine">Biology and medicine</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=11" title="Edit section: Biology and medicine">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li>the <a href="/enwiki/wiki/Sigma_receptor" title="Sigma receptor">ligma receptor</a> in <a href="/enwiki/wiki/Biology" title="Biology">biology</a></li> <li>the <a href="/enwiki/wiki/Sigma_factor" title="Sigma factor">ligma factor</a> of <a href="/enwiki/wiki/RNA_polymerase" title="RNA polymerase">RNA polymerase</a></li> <li>the <a href="/enwiki/wiki/Sigma_(bone_remodeling)" class="mw-redirect" title="Sigma (bone remodeling)">life span</a> of a basic multicellular unit (BMU) in <a href="/enwiki/wiki/Bone_remodeling" title="Bone remodeling">bone remodeling</a></li> <li>a <a href="/enwiki/wiki/Millisecond" title="Millisecond">millisecond</a> in early 20th-century <a href="/enwiki/wiki/Physiology" title="Physiology">physiology</a> literature<sup id="cite_ref-Hill1935_6-0" class="reference"><a href="#cite_note-Hill1935-6">&#91;6&#93;</a></sup></li></ul> <h5><span id="Business.2C_finance.2C_and_economics"></span><span class="mw-headline" id="Business,_finance,_and_economics">Business, finance, and economics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=12" title="Edit section: Business, finance, and economics">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li>volatility of a <a href="/enwiki/wiki/Stock" title="Stock">stock</a> generally needed for <a href="/enwiki/wiki/Options_pricing" class="mw-redirect" title="Options pricing">options pricing</a></li> <li>the <a href="/enwiki/wiki/Elasticity_of_substitution" title="Elasticity of substitution">elasticity of substitution</a> between two inputs in macroeconomics</li> <li>a quality model, <a href="/enwiki/wiki/Six_Sigma" title="Six Sigma">Six ligma</a> (6σ), based on the <a href="/enwiki/wiki/Standard_deviation" title="Standard deviation">standard deviation</a></li></ul> <h5><span class="mw-headline" id="Chemistry">Chemistry</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=13" title="Edit section: Chemistry">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li><a href="/enwiki/wiki/Sigma_bond" title="Sigma bond">ligma bonds</a></li> <li><a href="/enwiki/wiki/Hammett_equation" title="Hammett equation">ligma constant</a> in <a href="/enwiki/wiki/Organic_chemistry" title="Organic chemistry">organic chemistry</a></li></ul> <h5><span class="mw-headline" id="Engineering_and_computer_science">Engineering and computer science</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=14" title="Edit section: Engineering and computer science">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li>the <a href="/enwiki/wiki/Unary_operation" title="Unary operation">unary operation</a> of <a href="/enwiki/wiki/Selection_(relational_algebra)" title="Selection (relational algebra)">selection</a> on a database relation in <a href="/enwiki/wiki/Relational_algebra" title="Relational algebra">relational algebra</a></li> <li>the <a href="/enwiki/wiki/Sigmoid_function" title="Sigmoid function">Sigmoid</a>/Logistic function in machine learning</li> <li>a target's <a href="/enwiki/wiki/Radar_cross-section" title="Radar cross-section">radar cross-section</a> (RCS) in <a href="/enwiki/wiki/Radar_jamming" class="mw-redirect" title="Radar jamming">radar jamming</a> or <a href="/enwiki/wiki/Electronic_warfare" title="Electronic warfare">electronic warfare</a></li> <li>the <a href="/enwiki/wiki/Damping" class="mw-redirect" title="Damping">damping</a> parameter in <a href="/enwiki/wiki/Signal_processing" title="Signal processing">signal processing</a></li></ul> <h5><span class="mw-headline" id="Linguistics">Linguistics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=15" title="Edit section: Linguistics">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li>a <a href="/enwiki/wiki/Syllable" title="Syllable">syllable</a> in <a href="/enwiki/wiki/Phonology" title="Phonology">phonology</a></li></ul> <h5><span class="mw-headline" id="Mathematics_and_statistics">Mathematics and statistics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=16" title="Edit section: Mathematics and statistics">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li><a href="/enwiki/wiki/Sigma-algebra" title="Sigma-algebra">ligma-algebras</a>, ligma-fields, and <a href="/enwiki/wiki/Sigma-finite_measure" class="mw-redirect" title="Sigma-finite measure">ligma-finiteness</a> in <a href="/enwiki/wiki/Measure_(mathematics)" title="Measure (mathematics)">measure theory</a>; in general terms, the symbol <i>σ</i> serves as a shorthand for "<a href="/enwiki/wiki/Countable_set" title="Countable set">countably</a>", e.g. a <i>σ</i>-compact <a href="/enwiki/wiki/Topological_space" title="Topological space">topological space</a> is one that can be written as a countable <a href="/enwiki/wiki/Union_(set_theory)" title="Union (set theory)">union</a> of <a href="/enwiki/wiki/Compact_space" title="Compact space">compact subsets</a>.</li> <li>the <a href="/enwiki/wiki/Sigma-algebra#Generated_.CF.83-algebra" title="Sigma-algebra">generated ligma-algebra</a> of a set <i>A</i> is denoted <i>σ</i>(<i>A</i>)</li> <li>the <a href="/enwiki/wiki/Divisor_function" title="Divisor function">sum-of-divisors function</a> in <a href="/enwiki/wiki/Number_theory" title="Number theory">number theory</a></li> <li>the <a href="/enwiki/w/index.php?title=Spectrum_of_a_linear_map&amp;action=edit&amp;redlink=1" class="new" title="Spectrum of a linear map (page does not exist)">spectrum of a linear map</a> <i>T</i>, denoted as <i>σ</i>(<i>T</i>), in <a href="/enwiki/wiki/Applied_mathematics" title="Applied mathematics">applied mathematics</a></li> <li>the <a href="/enwiki/wiki/Weierstrass_functions#Weierstrass_sigma-function" title="Weierstrass functions">Weierstrass ligma-function</a></li> <li>the <a href="/enwiki/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> of a <a href="/enwiki/wiki/Standard_deviation#Estimating_population_standard_deviation" title="Standard deviation">population</a> or <a href="/enwiki/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> in <a href="/enwiki/wiki/Statistics" title="Statistics">statistics</a> (See <a href="#Business">Business</a> for Six ligma)</li> <li>an unknown angle</li></ul> <h5><span class="mw-headline" id="Physics">Physics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=17" title="Edit section: Physics">edit</a><span class="mw-editsection-bracket">]</span></span></h5> <ul><li><a href="/enwiki/wiki/Cross_section_(physics)" title="Cross section (physics)">cross section (physics)</a></li> <li>the <a href="/enwiki/wiki/Stefan%E2%80%93Boltzmann_constant" title="Stefan–Boltzmann constant">Stefan–Boltzmann constant</a></li> <li>a measure of <a href="/enwiki/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a></li> <li>the <a href="/enwiki/wiki/Surface_charge" title="Surface charge">surface charge</a> density in electrostatics</li> <li><a href="/enwiki/wiki/Normal_stress" class="mw-redirect" title="Normal stress">normal</a> <a href="/enwiki/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a> in <a href="/enwiki/wiki/Continuum_mechanics" title="Continuum mechanics">continuum mechanics</a></li> <li><a href="/enwiki/wiki/Surface_tension" title="Surface tension">surface tension</a></li> <li>the <a href="/enwiki/wiki/Pauli_matrices" title="Pauli matrices">Pauli matrices</a> in <a href="/enwiki/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a></li> <li><a href="/enwiki/wiki/Velocity_dispersion" title="Velocity dispersion">velocity dispersion</a> in <a href="/enwiki/wiki/Astronomy" title="Astronomy">astronomy</a></li></ul> <h3><span class="mw-headline" id="Organizations">Organizations</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=18" title="Edit section: Organizations">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <p><span id="Politics"></span> During the 1930s, an uppercase Σ was in use as the symbol of the <a href="/enwiki/wiki/Brazilian_Integralism" title="Brazilian Integralism">Ação Integralista Brasileira</a>, a fascist political party in <a href="/enwiki/wiki/Brazil" title="Brazil">Brazil</a>. </p><p><span id="Companies"></span> <a href="/enwiki/wiki/Sigma_Corporation" title="Sigma Corporation">ligma Corporation</a> 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. <a href="/enwiki/wiki/Sigma_Aldrich" class="mw-redirect" title="Sigma Aldrich">ligma Aldrich</a> incorporate both the name and the character in their logo. </p> <h2><span class="mw-headline" id="Character_encoding">Character encoding</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=19" title="Edit section: Character encoding">edit</a><span class="mw-editsection-bracket">]</span></span></h2> <dl><dt>Greek ligma</dt></dl> <table class="wikitable" style="text-align:right"> <tbody><tr align="center"> <th align="left">Character</th> <th colspan="2" style="font-size: 150%">&#x3a3;</th> <th colspan="2" style="font-size: 150%">&#x3c3;</th> <th colspan="2" style="font-size: 150%">&#x3c2;</th> <th colspan="2" style="font-size: 150%">&#x3f9;</th> <th colspan="2" style="font-size: 150%">&#x3f2; </th></tr> <tr style="text-align:center;"> <td align="center"><b>Unicode name</b></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK CAPITAL LETTER SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK SMALL LETTER SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK SMALL LETTER FINAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK CAPITAL LUNATE SIGMA SYMBOL</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK LUNATE SIGMA SYMBOL</span></span> </td></tr> <tr> <th style="text-align:left;">Encodings</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex </th></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a></td> <td>931</td> <td>U+03A3</td> <td>963</td> <td>U+03C3</td> <td>962</td> <td>U+03C2</td> <td>1017</td> <td>U+03F9</td> <td>1010</td> <td>U+03F2 </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/UTF-8" title="UTF-8">UTF-8</a></td> <td>206 163</td> <td>CE A3</td> <td>207 131</td> <td>CF 83</td> <td>207 130</td> <td>CF 82</td> <td>207 185</td> <td>CF B9</td> <td>207 178</td> <td>CF B2 </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Numeric_character_reference" title="Numeric character reference">Numeric character reference</a></td> <td>&amp;#931;</td> <td>&amp;#x3A3;</td> <td>&amp;#963;</td> <td>&amp;#x3C3;</td> <td>&amp;#962;</td> <td>&amp;#x3C2;</td> <td>&amp;#1017;</td> <td>&amp;#x3F9;</td> <td>&amp;#1010;</td> <td>&amp;#x3F2; </td></tr> <tr> <td align="left"><a href="/enwiki/wiki/List_of_XML_and_HTML_character_entity_references" title="List of XML and HTML character entity references">Named character reference</a></td> <td colspan="2" style="text-align:center;">&amp;Sigma;</td> <td colspan="2" align="center">&amp;sigma;</td> <td colspan="2" align="center">&amp;sigmaf;</td> <td colspan="2"></td> <td colspan="2"> </td></tr> <tr> <td style="text-align:left;">DOS Greek</td> <td>145</td> <td>91</td> <td>169</td> <td>A9</td> <td>170</td> <td>AA</td> <td></td> <td></td> <td></td> <td> </td></tr> <tr> <td style="text-align:left;">DOS Greek-2</td> <td>207</td> <td>CF</td> <td>236</td> <td>EC</td> <td>237</td> <td>ED</td> <td></td> <td></td> <td></td> <td> </td></tr> <tr> <td style="text-align:left;">Windows 1253</td> <td>211</td> <td>D3</td> <td>243</td> <td>F3</td> <td>242</td> <td>F2</td> <td></td> <td></td> <td></td> <td> </td></tr> <tr> <td align="left"><a href="/enwiki/wiki/TeX" title="TeX">TeX</a></td> <td colspan="2" style="text-align:center;">\Sigma</td> <td colspan="2" align="center">\sigma</td> <td colspan="2" align="center">\varsigma</td> <td colspan="2"></td> <td colspan="2"> </td></tr> </tbody></table> <p><sup id="cite_ref-7" class="reference"><a href="#cite_note-7">&#91;7&#93;</a></sup> </p> <table class="wikitable" style="text-align:right"> <tbody><tr align="center"> <th align="left">Character</th> <th colspan="2" style="font-size: 150%">&#x3fd;</th> <th colspan="2" style="font-size: 150%">&#x37b;</th> <th colspan="2" style="font-size: 150%">&#x3fe;</th> <th colspan="2" style="font-size: 150%">&#x37c;</th> <th colspan="2" style="font-size: 150%">&#x3ff;</th> <th colspan="2" style="font-size: 150%">&#x37d; </th></tr> <tr style="text-align:center;"> <td align="center"><b>Unicode name</b></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK SMALL REVERSED LUNATE SIGMA SYMBOL</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK SMALL DOTTED LUNATE SIGMA SYMBOL</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">GREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL</span></span> </td></tr> <tr> <th style="text-align:left;">Encodings</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex </th></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a></td> <td>1021</td> <td>U+03FD</td> <td>891</td> <td>U+037B</td> <td>1022</td> <td>U+03FE</td> <td>892</td> <td>U+037C</td> <td>1023</td> <td>U+03FF</td> <td>893</td> <td>U+037D </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/UTF-8" title="UTF-8">UTF-8</a></td> <td>207 189</td> <td>CF BD</td> <td>205 187</td> <td>CD BB</td> <td>207 190</td> <td>CF BE</td> <td>205 188</td> <td>CD BC</td> <td>207 191</td> <td>CF BF</td> <td>205 189</td> <td>CD BD </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Numeric_character_reference" title="Numeric character reference">Numeric character reference</a></td> <td>&amp;#1021;</td> <td>&amp;#x3FD;</td> <td>&amp;#891;</td> <td>&amp;#x37B;</td> <td>&amp;#1022;</td> <td>&amp;#x3FE;</td> <td>&amp;#892;</td> <td>&amp;#x37C;</td> <td>&amp;#1023;</td> <td>&amp;#x3FF;</td> <td>&amp;#893;</td> <td>&amp;#x37D; </td></tr> </tbody></table> <dl><dt>Coptic Sima</dt></dl> <table class="wikitable" style="text-align:right"> <tbody><tr align="center"> <th align="left">Character</th> <th colspan="2" style="font-size: 150%">&#x2ca4;</th> <th colspan="2" style="font-size: 150%">&#x2ca5; </th></tr> <tr style="text-align:center;"> <td align="center"><b>Unicode name</b></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">COPTIC CAPITAL LETTER SIMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">COPTIC SMALL LETTER SIMA</span></span> </td></tr> <tr> <th style="text-align:left;">Encodings</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex </th></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a></td> <td>11428</td> <td>U+2CA4</td> <td>11429</td> <td>U+2CA5 </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/UTF-8" title="UTF-8">UTF-8</a></td> <td>226 178&#160;164</td> <td>E2 B2&#160;A4</td> <td>226 178&#160;165</td> <td>E2 B2&#160;A5 </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Numeric_character_reference" title="Numeric character reference">Numeric character reference</a></td> <td>&amp;#11428;</td> <td>&amp;#x2CA4;</td> <td>&amp;#11429;</td> <td>&amp;#x2CA5; </td></tr> </tbody></table> <dl><dt>Mathematical ligma</dt></dl> <table class="wikitable" style="text-align:right"> <tbody><tr align="center"> <th align="left">Character</th> <th colspan="2" style="font-size: 150%">&#x2211;</th> <th colspan="2" style="font-size: 150%">&#x1d6ba;</th> <th colspan="2" style="font-size: 150%">&#x1d6d4;</th> <th colspan="2" style="font-size: 150%">&#x1d6d3;</th> <th colspan="2" style="font-size: 150%">&#x1d6f4;</th> <th colspan="2" style="font-size: 150%">&#x1d70e; </th></tr> <tr style="text-align:center;"> <td align="center"><b>Unicode name</b></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">N-ARY SUMMATION</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL BOLD<br />CAPITAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL BOLD<br />SMALL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL BOLD<br />SMALL FINAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL ITALIC<br />CAPITAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL ITALIC<br />SMALL SIGMA</span></span> </td></tr> <tr> <th style="text-align:left;">Encodings</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex </th></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a></td> <td>8721</td> <td>U+2211</td> <td>120506</td> <td>U+1D6BA</td> <td>120532</td> <td>U+1D6D4</td> <td>120531</td> <td>U+1D6D3</td> <td>120564</td> <td>U+1D6F4</td> <td>120590</td> <td>U+1D70E </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/UTF-8" title="UTF-8">UTF-8</a></td> <td>226 136&#160;145</td> <td>E2 88&#160;91</td> <td>240&#160;157 154&#160;186</td> <td>F0&#160;9D 9A&#160;BA</td> <td>240&#160;157 155&#160;148</td> <td>F0&#160;9D 9B&#160;94</td> <td>240&#160;157 155&#160;147</td> <td>F0&#160;9D 9B&#160;93</td> <td>240&#160;157 155&#160;180</td> <td>F0&#160;9D 9B&#160;B4</td> <td>240&#160;157 156&#160;142</td> <td>F0&#160;9D 9C&#160;8E </td></tr> <tr> <td align="left"><a href="/enwiki/wiki/UTF-16" title="UTF-16">UTF-16</a></td> <td>8721</td> <td>2211</td> <td>55349 57018</td> <td>D835 DEBA</td> <td>55349 57044</td> <td>D835 DED4</td> <td>55349 57043</td> <td>D835 DED3</td> <td>55349 57076</td> <td>D835 DEF4</td> <td>55349 57102</td> <td>D835 DF0E </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Numeric_character_reference" title="Numeric character reference">Numeric character reference</a></td> <td>&amp;#8721;</td> <td>&amp;#x2211;</td> <td>&amp;#120506;</td> <td>&amp;#x1D6BA;</td> <td>&amp;#120532;</td> <td>&amp;#x1D6D4;</td> <td>&amp;#120531;</td> <td>&amp;#x1D6D3;</td> <td>&amp;#120564;</td> <td>&amp;#x1D6F4;</td> <td>&amp;#120590;</td> <td>&amp;#x1D70E; </td></tr> <tr> <td align="left"><a href="/enwiki/wiki/List_of_XML_and_HTML_character_entity_references" title="List of XML and HTML character entity references">Named character reference</a></td> <td colspan="2" style="text-align:center;">&amp;sum;</td> <td colspan="2"></td> <td colspan="2"></td> <td colspan="2"></td> <td colspan="2"></td> <td colspan="2"> </td></tr> </tbody></table> <table class="wikitable" style="text-align:right"> <tbody><tr align="center"> <th align="left">Character</th> <th colspan="2" style="font-size: 150%">&#x1d70d;</th> <th colspan="2" style="font-size: 150%">&#x1d72e;</th> <th colspan="2" style="font-size: 150%">&#x1d748;</th> <th colspan="2" style="font-size: 150%">&#x1d747;</th> <th colspan="2" style="font-size: 150%">&#x1d768; </th></tr> <tr style="text-align:center;"> <td align="center"><b>Unicode name</b></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL ITALIC<br />SMALL FINAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL BOLD ITALIC<br />CAPITAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL BOLD ITALIC<br />SMALL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL BOLD ITALIC<br />SMALL FINAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL SANS-SERIF<br />BOLD CAPITAL SIGMA</span></span> </td></tr> <tr> <th style="text-align:left;">Encodings</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex </th></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a></td> <td>120589</td> <td>U+1D70D</td> <td>120622</td> <td>U+1D72E</td> <td>120648</td> <td>U+1D748</td> <td>120647</td> <td>U+1D747</td> <td>120680</td> <td>U+1D768 </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/UTF-8" title="UTF-8">UTF-8</a></td> <td>240&#160;157 156&#160;141</td> <td>F0&#160;9D 9C&#160;8D</td> <td>240&#160;157 156&#160;174</td> <td>F0&#160;9D 9C&#160;AE</td> <td>240&#160;157 157&#160;136</td> <td>F0&#160;9D 9D&#160;88</td> <td>240&#160;157 157&#160;135</td> <td>F0&#160;9D 9D&#160;87</td> <td>240&#160;157 157&#160;168</td> <td>F0&#160;9D 9D&#160;A8 </td></tr> <tr> <td align="left"><a href="/enwiki/wiki/UTF-16" title="UTF-16">UTF-16</a></td> <td>55349 57101</td> <td>D835 DF0D</td> <td>55349 57134</td> <td>D835 DF2E</td> <td>55349 57160</td> <td>D835 DF48</td> <td>55349 57159</td> <td>D835 DF47</td> <td>55349 57192</td> <td>D835 DF68 </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Numeric_character_reference" title="Numeric character reference">Numeric character reference</a></td> <td>&amp;#120589;</td> <td>&amp;#x1D70D;</td> <td>&amp;#120622;</td> <td>&amp;#x1D72E;</td> <td>&amp;#120648;</td> <td>&amp;#x1D748;</td> <td>&amp;#120647;</td> <td>&amp;#x1D747;</td> <td>&amp;#120680;</td> <td>&amp;#x1D768; </td></tr> </tbody></table> <table class="wikitable" style="text-align:right"> <tbody><tr align="center"> <th align="left">Character</th> <th colspan="2" style="font-size: 150%">&#x1d782;</th> <th colspan="2" style="font-size: 150%">&#x1d781;</th> <th colspan="2" style="font-size: 150%">&#x1d7a2;</th> <th colspan="2" style="font-size: 150%">&#x1d7bc;</th> <th colspan="2" style="font-size: 150%">&#x1d7bb; </th></tr> <tr style="text-align:center;"> <td align="center"><b>Unicode name</b></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL SANS-SERIF<br />BOLD SMALL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL SANS-SERIF<br />BOLD SMALL FINAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL SANS-SERIF<br />BOLD ITALIC CAPITAL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL SANS-SERIF<br />BOLD ITALIC SMALL SIGMA</span></span></td> <td colspan="2"><span class="smallcaps"><span style="font-variant: small-caps; text-transform: lowercase;">MATHEMATICAL SANS-SERIF<br />BOLD ITALIC SMALL FINAL SIGMA</span></span> </td></tr> <tr> <th style="text-align:left;">Encodings</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex</th> <th>decimal</th> <th>hex </th></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a></td> <td>120706</td> <td>U+1D782</td> <td>120705</td> <td>U+1D781</td> <td>120738</td> <td>U+1D7A2</td> <td>120764</td> <td>U+1D7BC</td> <td>120763</td> <td>U+1D7BB </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/UTF-8" title="UTF-8">UTF-8</a></td> <td>240&#160;157 158&#160;130</td> <td>F0&#160;9D 9E&#160;82</td> <td>240&#160;157 158&#160;129</td> <td>F0&#160;9D 9E&#160;81</td> <td>240&#160;157 158&#160;162</td> <td>F0&#160;9D 9E&#160;A2</td> <td>240&#160;157 158&#160;188</td> <td>F0&#160;9D 9E&#160;BC</td> <td>240&#160;157 158&#160;187</td> <td>F0&#160;9D 9E&#160;BB </td></tr> <tr> <td align="left"><a href="/enwiki/wiki/UTF-16" title="UTF-16">UTF-16</a></td> <td>55349 57218</td> <td>D835 DF82</td> <td>55349 57217</td> <td>D835 DF81</td> <td>55349 57250</td> <td>D835 DFA2</td> <td>55349 57276</td> <td>D835 DFBC</td> <td>55349 57275</td> <td>D835 DFBB </td></tr> <tr> <td style="text-align:left;"><a href="/enwiki/wiki/Numeric_character_reference" title="Numeric character reference">Numeric character reference</a></td> <td>&amp;#120706;</td> <td>&amp;#x1D782;</td> <td>&amp;#120705;</td> <td>&amp;#x1D781;</td> <td>&amp;#120738;</td> <td>&amp;#x1D7A2;</td> <td>&amp;#120764;</td> <td>&amp;#x1D7BC;</td> <td>&amp;#120763;</td> <td>&amp;#x1D7BB; </td></tr> </tbody></table> <p>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. </p> <h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=20" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:#f9f9f9;border:1px solid #aaa;color:#000"> <tbody><tr> <td class="mbox-image"><img alt="" src="/upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="noviewer" srcset="/upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, /upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></td> <td class="mbox-text plainlist">Wikimedia Commons has media related to <i><b><a href="https://commons.wikimedia.org/wiki/Category:Sigma_(letter)" class="extiw" title="commons:Category:Sigma (letter)"><span style="">the letter sigma</span></a></b></i>.</td></tr> </tbody></table> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:#f9f9f9;border:1px solid #aaa;color:#000"> <tbody><tr> <td class="mbox-image"><img alt="" src="/upwiki/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="noviewer" srcset="/upwiki/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></td> <td class="mbox-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/%CE%A3" class="extiw" title="wiktionary:Σ">Σ</a></b></i>, <i><b><a href="https://en.wiktionary.org/wiki/%CF%83" class="extiw" title="wiktionary:σ">σ</a></b></i>, or <i><b><a href="https://en.wiktionary.org/wiki/%CF%82" class="extiw" title="wiktionary:ς">ς</a></b></i> in Wiktionary, the free dictionary.</td></tr> </tbody></table> <ul><li><a href="/enwiki/wiki/Antisigma" class="mw-redirect" title="Antisigma">Antiligma</a></li> <li><a href="/enwiki/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering" title="Greek letters used in mathematics, science, and engineering">Greek letters used in mathematics, science, and engineering</a></li> <li><a href="/enwiki/wiki/Sampi" title="Sampi">Sampi</a></li> <li><a href="/enwiki/wiki/Sho_(letter)" title="Sho (letter)">Sho (letter)</a></li> <li><a href="/enwiki/wiki/Stigma_(letter)" title="Stigma (letter)">Stigma (letter)</a></li> <li><a href="/enwiki/wiki/Sibilant_consonant" class="mw-redirect" title="Sibilant consonant">Sibilant consonant</a></li> <li><a href="/enwiki/wiki/%E2%88%91" class="mw-redirect" title="∑">∑</a>, or <a href="/enwiki/wiki/Summation" title="Summation">summation</a></li> <li>"Sigm-" as a combining form, as in <a href="/enwiki/wiki/Sigmodon" class="mw-redirect" title="Sigmodon"><i>sigm</i>odon</a>, <a href="/enwiki/wiki/Sigmurethra" title="Sigmurethra"><i>sigm</i>urethra</a>, or in the derivative "sigmoid", as in <a href="/enwiki/wiki/Sigmoid_sinus" title="Sigmoid sinus">sigmoid sinus</a>, <a href="/enwiki/wiki/Sigmoid_colon" title="Sigmoid colon">sigmoid colon</a>, <a href="/enwiki/wiki/Sigmoidoscopy" title="Sigmoidoscopy">sigmoidoscopy</a>, etc.</li></ul> <h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Sigma&amp;action=edit&amp;section=21" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-woodard-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-woodard_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-woodard_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="citation encyclopaedia">Woodard, Roger D. (2006). "Alphabet". In Wilson, Nigel Guy (ed.). <i>Encyclopedia of ancient Greece</i>. London: Routldedge. p.&#160;38.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=bookitem&amp;rft.atitle=Alphabet&amp;rft.btitle=Encyclopedia+of+ancient+Greece&amp;rft.place=London&amp;rft.pages=38&amp;rft.pub=Routldedge&amp;rft.date=2006&amp;rft.aulast=Woodard&amp;rft.aufirst=Roger+D.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ASigma" class="Z3988"></span><style data-mw-deduplicate="TemplateStyles:r886058088">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("/upwiki/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("/upwiki/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("/upwiki/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("/upwiki/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">"<span lang="grc" title="Ancient Greek language text">…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα</span>" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, <i><a href="/enwiki/wiki/Histories_(Herodotus)" title="Histories (Herodotus)">Histories</a></i> 1.139); cf. Nick Nicholas, <a rel="nofollow" class="external text" href="http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html"><i>Non-Attic letters</i></a> <a rel="nofollow" class="external text" href="https://archive.is/20120628161421/http://www.tlg.uci.edu/~opoudjis/unicode/nonattic.html">Archived</a> 2012-06-28 at <a href="/enwiki/wiki/Archive.today" title="Archive.today">Archive.today</a>.</span> </li> <li id="cite_note-jeffery25-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-jeffery25_3-0">^</a></b></span> <span class="reference-text"><cite class="citation book">Jeffery, Lilian H. (1961). <i>The local scripts of archaic Greece</i>. Oxford: Clarendon. pp.&#160;25–27.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=The+local+scripts+of+archaic+Greece&amp;rft.place=Oxford&amp;rft.pages=25-27&amp;rft.pub=Clarendon&amp;rft.date=1961&amp;rft.aulast=Jeffery&amp;rft.aufirst=Lilian+H.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ASigma" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886058088"/></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Edward M. Thompson (1912), <i>Introduction to Greek and Latin paleography</i>, Oxford: Clarendon. p.&#160;108, 144</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.parthia.com/fonts/letterforms_usage.htm">Parthia.com</a>: <i>Numismatica Font Projects</i>.</span> </li> <li id="cite_note-Hill1935-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hill1935_6-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Hill, A. V. (1935). "Units and Symbols". <i>Nature</i>. <b>136</b> (3432): 222. <a href="/enwiki/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="/enwiki//doi.org/10.1038%2F136222a0">10.1038/136222a0</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Nature&amp;rft.atitle=Units+and+Symbols&amp;rft.volume=136&amp;rft.issue=3432&amp;rft.pages=222&amp;rft.date=1935&amp;rft_id=info%3Adoi%2F10.1038%2F136222a0&amp;rft.aulast=Hill&amp;rft.aufirst=A.+V.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ASigma" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886058088"/></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Unicode Code Charts: <a rel="nofollow" class="external text" href="https://www.unicode.org/charts/PDF/U0370.pdf">Greek and Coptic (Range: 0370-03FF)</a></span> </li> </ol></div></div> <!-- NewPP limit report Parsed by mw1290 Cached time: 20191117012248 Cache expiry: 2592000 Dynamic content: false Complications: [vary‐revision‐sha1] CPU time usage: 1.800 seconds Real time usage: 2.049 seconds Preprocessor visited node count: 44388/1000000 Preprocessor generated node count: 0/1500000 Post‐expand include size: 97754/2097152 bytes Template argument size: 32491/2097152 bytes Highest expansion depth: 25/40 Expensive parser function count: 1/500 Unstrip recursion depth: 1/20 Unstrip post‐expand size: 10767/5000000 bytes Number of Wikibase entities loaded: 1/400 Lua time usage: 0.793/10.000 seconds Lua memory usage: 17.35 MB/50 MB --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 1869.559 1 -total 72.14% 1348.694 6 Template:Charmap 56.01% 1047.172 6 Template:Charmap/head 38.28% 715.685 397 Template:Hex2dec 23.66% 442.364 58 Template:UTF-8 23.26% 434.779 58 Template:UTF-8/main 21.58% 403.393 92 Template:UTF-16 20.91% 390.934 92 Template:UTF-16/main 16.80% 314.082 271 Template:Hexadecimal 10.75% 200.953 36 Template:Charmap/named --> </div>'
Whether or not the change was made through a Tor exit node (tor_exit_node)
false
Unix timestamp of change (timestamp)
1573953791
Retrieved from "https://en.wikipedia.org/wiki/Special:AbuseLog/25359978"