Sigma
Sigma (uppercase Σ, lowercase σ, lowercase in wordfinal position ς; Greek: 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. Ὀδυσσεύς (Odysseus); note the two sigmas in the center of the name, and the wordfinal sigma at the end.
Greek alphabet  



History  
Use in other languages  
Related topics  
 
History
The shape Σς and alphabetic position of sigma is derived from Phoenician shin 𐤔
The name "sigma", according to one hypothesis,[3] may continue that of Phoenician Samekh, the letter continued by Greek Ξ. Alternatively, the name sigma may have been a Greek innovation that simply meant "hissing", from the root of σίζω (sízō, earlier *sigjō, meaning "I hiss").[1]
Lunate sigma
In handwritten Greek during the Hellenistic period (4th and 3rd centuries BC), the epigraphic form of Σ was simplified into a Clike shape.[4] It is also found on coins from the fourth century BC onward.[5] 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 crescentlike 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 threestroke version, omitting the lowermost stroke, is found already in Western Greek alphabets, and becomes current in classical Etruscan, in Oscan, and also in the earliest Latin epigraphy (early Latin S), such as the Duenos inscription. The alternation between three and four strokes (occasionally also more than four) is also adopted into the early runic alphabet (early form of the srune. Both the AngloSaxon runes and the Younger Futhark consistently use the simplified threestroke version.
The forms of the Coptic letter Ⲥ sima (2nd century BC) and of Cyrillic letter С (9th century) are derived from lunate sigma.
Uses
Greek
In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative /s/. In Modern Greek, this sound is voiced to /z/ before /m/, /n/, /v/, /ð/ or /ɣ/.
International African Alphabet
The uppercase form of sigma was reborrowed into the Latin alphabet – more precisely, the International African Alphabet – to serve as the uppercase of modern esh (lowercase: ʃ).
Science and mathematics
Uppercase
Uppercase Σ is used as a symbol for:
 the summation operator
 e.g.:
 a class of baryons in particle physics
 macroscopic cross sections in nuclear and particle physics
 selfenergy in condensed matter physics
 the balance of the invoice classes and the overall amount of the debts and demands in economics
 the set of symbols that form an alphabet in linguistics and computer science
 the covariance matrix of a set of random variables in probability theory and statistics, sometimes in the form 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 life span of a basic multicellular unit (BMU) in bone remodeling
 a millisecond in early 20thcentury physiology literature[6]
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
Engineering and computer science
 the unary operation of selection on a database relation in relational algebra
 the Sigmoid/Logistic function in machine learning
 a target's radar crosssection (RCS) in radar jamming or electronic warfare
 the damping parameter in signal processing
Mathematics and statistics
 sigmaalgebras, sigmafields, and sigmafiniteness in measure theory; in general terms, the symbol σ serves as a shorthand for "countably", e.g. a σcompact topological space is one that can be written as a countable union of compact subsets.
 the generated sigmaalgebra of a set A is denoted σ(A)
 the sumofdivisors function in number theory
 the spectrum of a linear map T, denoted as σ(T), in applied mathematics
 the Weierstrass sigmafunction
 the standard deviation of a population or probability distribution in statistics (See 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 in continuum mechanics
 surface tension
 the Pauli matrices in quantum mechanics
 velocity dispersion in astronomy
Organizations
During the 1930s, an uppercase Σ was in use as the symbol of the Ação Integralista Brasileira, a fascist political party in Brazil.
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
Character  Σ  σ  ς  Ϲ  ϲ  

Unicode name  GREEK CAPITAL LETTER SIGMA  GREEK SMALL LETTER SIGMA  GREEK SMALL LETTER FINAL SIGMA  GREEK CAPITAL LUNATE SIGMA SYMBOL  GREEK LUNATE SIGMA SYMBOL  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  931  U+03A3  963  U+03C3  962  U+03C2  1017  U+03F9  1010  U+03F2 
UTF8  206 163  CE A3  207 131  CF 83  207 130  CF 82  207 185  CF B9  207 178  CF B2 
Numeric character reference  Σ  Σ  σ  σ  ς  ς  Ϲ  Ϲ  ϲ  ϲ 
Named character reference  Σ  σ  ς  
DOS Greek  145  91  169  A9  170  AA  
DOS Greek2  207  CF  236  EC  237  ED  
Windows 1253  211  D3  243  F3  242  F2  
TeX  \Sigma  \sigma  \varsigma 
Character  Ͻ  ͻ  Ͼ  ͼ  Ͽ  ͽ  

Unicode name  GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL  GREEK SMALL REVERSED LUNATE SIGMA SYMBOL  GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL  GREEK SMALL DOTTED LUNATE SIGMA SYMBOL  GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL  GREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  1021  U+03FD  891  U+037B  1022  U+03FE  892  U+037C  1023  U+03FF  893  U+037D 
UTF8  207 189  CF BD  205 187  CD BB  207 190  CF BE  205 188  CD BC  207 191  CF BF  205 189  CD BD 
Numeric character reference  Ͻ  Ͻ  ͻ  ͻ  Ͼ  Ͼ  ͼ  ͼ  Ͽ  Ͽ  ͽ  ͽ 
 Coptic Sima
Character  Ⲥ  ⲥ  

Unicode name  COPTIC CAPITAL LETTER SIMA  COPTIC SMALL LETTER SIMA  
Encodings  decimal  hex  decimal  hex 
Unicode  11428  U+2CA4  11429  U+2CA5 
UTF8  226 178 164  E2 B2 A4  226 178 165  E2 B2 A5 
Numeric character reference  Ⲥ  Ⲥ  ⲥ  ⲥ 
 Mathematical Sigma
Character  ∑  𝚺  𝛔  𝛓  𝛴  𝜎  

Unicode name  NARY SUMMATION  MATHEMATICAL BOLD CAPITAL SIGMA  MATHEMATICAL BOLD SMALL SIGMA  MATHEMATICAL BOLD SMALL FINAL SIGMA  MATHEMATICAL ITALIC CAPITAL SIGMA  MATHEMATICAL ITALIC SMALL SIGMA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  8721  U+2211  120506  U+1D6BA  120532  U+1D6D4  120531  U+1D6D3  120564  U+1D6F4  120590  U+1D70E 
UTF8  226 136 145  E2 88 91  240 157 154 186  F0 9D 9A BA  240 157 155 148  F0 9D 9B 94  240 157 155 147  F0 9D 9B 93  240 157 155 180  F0 9D 9B B4  240 157 156 142  F0 9D 9C 8E 
UTF16  8721  2211  55349 57018  D835 DEBA  55349 57044  D835 DED4  55349 57043  D835 DED3  55349 57076  D835 DEF4  55349 57102  D835 DF0E 
Numeric character reference  ∑  ∑  𝚺  𝚺  𝛔  𝛔  𝛓  𝛓  𝛴  𝛴  𝜎  𝜎 
Named character reference  ∑ 
Character  𝜍  𝜮  𝝈  𝝇  𝝨  

Unicode name  MATHEMATICAL ITALIC SMALL FINAL SIGMA  MATHEMATICAL BOLD ITALIC CAPITAL SIGMA  MATHEMATICAL BOLD ITALIC SMALL SIGMA  MATHEMATICAL BOLD ITALIC SMALL FINAL SIGMA  MATHEMATICAL SANSSERIF BOLD CAPITAL SIGMA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120589  U+1D70D  120622  U+1D72E  120648  U+1D748  120647  U+1D747  120680  U+1D768 
UTF8  240 157 156 141  F0 9D 9C 8D  240 157 156 174  F0 9D 9C AE  240 157 157 136  F0 9D 9D 88  240 157 157 135  F0 9D 9D 87  240 157 157 168  F0 9D 9D A8 
UTF16  55349 57101  D835 DF0D  55349 57134  D835 DF2E  55349 57160  D835 DF48  55349 57159  D835 DF47  55349 57192  D835 DF68 
Numeric character reference  𝜍  𝜍  𝜮  𝜮  𝝈  𝝈  𝝇  𝝇  𝝨  𝝨 
Character  𝞂  𝞁  𝞢  𝞼  𝞻  

Unicode name  MATHEMATICAL SANSSERIF BOLD SMALL SIGMA  MATHEMATICAL SANSSERIF BOLD SMALL FINAL SIGMA  MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL SIGMA  MATHEMATICAL SANSSERIF BOLD ITALIC SMALL SIGMA  MATHEMATICAL SANSSERIF BOLD ITALIC SMALL FINAL SIGMA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120706  U+1D782  120705  U+1D781  120738  U+1D7A2  120764  U+1D7BC  120763  U+1D7BB 
UTF8  240 157 158 130  F0 9D 9E 82  240 157 158 129  F0 9D 9E 81  240 157 158 162  F0 9D 9E A2  240 157 158 188  F0 9D 9E BC  240 157 158 187  F0 9D 9E BB 
UTF16  55349 57218  D835 DF82  55349 57217  D835 DF81  55349 57250  D835 DFA2  55349 57276  D835 DFBC  55349 57275  D835 DFBB 
Numeric character reference  𝞂  𝞂  𝞁  𝞁  𝞢  𝞢  𝞼  𝞼  𝞻  𝞻 
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
Wikimedia Commons has media related to the letter sigma. 
Look up Σ, σ, or ς in Wiktionary, the free dictionary. 
 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, sigmurethra, or in the derivative "sigmoid", as in sigmoid sinus, sigmoid colon, sigmoidoscopy, etc.
References
 Woodard, Roger D. (2006). "Alphabet". In Wilson, Nigel Guy (ed.). Encyclopedia of ancient Greece. London: Routldedge. p. 38.
 "…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, Histories 1.139); cf. Nick Nicholas, NonAttic letters Archived 20120628 at Archive.today.
 Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 25–27.
 Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p. 108, 144
 Parthia.com: Numismatica Font Projects.
 Hill, A. V. (1935). "Units and Symbols". Nature. 136 (3432): 222. doi:10.1038/136222a0.
 Unicode Code Charts: Greek and Coptic (Range: 037003FF)