Sigma
{{#invoke:Hatnotehatnote}} Template:Sister
Greek alphabet  

Αα  Alpha  Νν  Nu 
Ββ  Beta  Ξξ  Xi 
Γγ  Gamma  Οο  Omicron 
Δδ  Delta  Ππ  Pi 
Εε  Epsilon  Ρρ  Rho 
Ζζ  Zeta  Σσς  Sigma 
Ηη  Eta  Ττ  Tau 
Θθ  Theta  Υυ  Upsilon 
Ιι  Iota  Φφ  Phi 
Κκ  Kappa  Χχ  Chi 
Λλ  Lambda  Ψψ  Psi 
Μμ  Mu  Ωω  Omega 
History  
Archaic local variants  
In other languages  
Scientific symbols  

Sigma (uppercase Σ, lowercase σ, lowercase in wordfinal position ς; Greek σίγμα) is the eighteenth letter of the Greek alphabet, and carries the 's' sound. 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 uppercase, 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.
Contents
History
The shape and alphabetic position of Sigma is derived from Phoenician shin 𐤔 .
Etymology
The name of sigma, according to one hypothesis,^{[1]} may continue that of Phoenician Samekh. According to a different theory,^{[2]} its original name may have been "San " (the name today associated with another, obsolete letter), while "sigma" was a Greek innovation that simply meant "hissing", based on a nominalization of a verb σίζω{{#invoke:Category handlermain}} (sízō, from earlier *sigjō, meaning 'I hiss').
Uppercase of esh
The uppercase form of sigma was reborrowed into the Latin alphabet to serve as the uppercase of modern esh (lowercase: ʃ).
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.^{[3]} It is also found on coins from the fourth century BC onward.^{[4]} 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. The forms of the Cyrillic letter С (representing /s/) and Coptic letter Template:Coptic sima are derived from lunate sigma.
A dotted lunate sigma (sigma periestigmenon, encoded at U+03FE Ͼ) was used by Aristarchus of Samothrace 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.
Uses
Greek
In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative /s/. Both in Ancient and Modern Greek, this sound is voiced to /z/ before /m/ or /n/.
Berber
Uppercase Σ may be used in the Berber Latin alphabet for [ʕ], though the INALCO standard uses Ɛ instead.
Science and mathematics
Uppercase
Uppercase Σ is used as a symbol for:
 the summation operator
 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:
 sigma bonds in chemistry
 to represent an unknown angle in mathematics
 Velocity dispersion in astronomy
 Sigma constant in science
 the sigma receptor in biology
 the standard deviation of a population or probability distribution in statistics
 a quality model for business, Six Sigma, based on the standard deviation, often referred to as "6σ"
 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 is denoted
 the sumofdivisors function in number theory
 the Stefan–Boltzmann constant
 the "sigma factor" of RNA polymerase
 a measure of electrical conductivity
 the Surface charge density in electrostatics
 Normal stress in continuum mechanics
 volatility of a stock generally needed for options pricing
 a syllable in phonology
 the spectrum of a matrix , denoted as , in applied mathematics
 surface tension
 the unary operation of selection on a database relation in relational algebra
 the Pauli matrices in quantum mechanics
 a target's radar crosssection (RCS) in radar jamming or Electronic Warfare (EW)
 the life span of a basic multicellular unit (BMU) in bone remodeling
 the Damping Parameter in Signal processing
 a millisecond in early 20thcentury physiology literature.^{[5]}
 The Weierstrass sigmafunction
Politics
During the 1930s, an uppercase Σ was in use as the symbol of the Ação Integralista Brasileira, a fascist political party in Brazil.
Companies
Sigma Corporation uses the name of the letter but not the letter itself, however in many Internet forums photographers refer to the company or its lenses using the sigma letter. Sigma Aldrich incorporate both the name and the character in their logo.
Character encodings
 Greek Sigma
Template:Charmap ^{[6]}
 Coptic Sima
 Mathematical 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
 Antisigma
 Greek letters used in mathematics, science, and engineering
 Sampi
 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
 ↑ {{#invoke:citation/CS1citation CitationClass=book }}
 ↑ {{#invoke:citation/CS1citation CitationClass=encyclopaedia }}
 ↑ Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p. 108, 144
 ↑ Parthia.com: Numismatica Font Projects.
 ↑ Template:Cite doi
 ↑ Unicode Code Charts: Greek and Coptic (Range: 037003FF)