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Sigma (upper case Σ, lower case σ, lower case in word-final 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, and the word is not all upper case, the final form (ς) is used, e.g. 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 shin 𐤔 .
Etymology
The name of sigma, according to one theory, may continue that of Phoenician Samekh. According to a different theory, 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 (sízō, from earlier *sig-jō, meaning 'I hiss').
Uppercase of esh
The uppercase form of sigma was re-borrowed 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 C-like shape. It is also found on coins from the fourth century BC onwards. This became the universal standard form of Sigma during late antiquity and the Middle Ages. It is today known as lunate sigma (upper case Ϲ, lower case 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. The forms of the Cyrillic letter С (representing /s/) and Coptic letter Ⲥ 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
Upper case Σ may be used in the Berber Latin alphabet for [ʕ], though the INALCO standard uses Ɛ instead.
Science and mathematics
Upper case
Upper case Σ is used as a symbol for:
the summation operatora class of baryons in particle physicsmacroscopic cross sections in nuclear and particle physicsself-energy in condensed matter physicsthe balance of the invoice classes and the overall amount of the debts and demands in economicsthe set of symbols that form an alphabet in linguistics and computer sciencethe covariance matrix of a set of random variables in probability theory and statistics, sometimes in the form to distinguish it from the summation operator.Lower case
Lower case σ is used for:
sigma bonds in chemistrySigma constant in sciencethe sigma receptor in biologythe standard deviation of a population or probability distribution in statisticsa quality model for business, Six Sigma, based on the standard deviation, often referred to as "6σ"sigma-algebras, sigma-fields and sigma-finiteness in measure theory; more generally, the symbol σ serves as a shorthand for "countably", e.g. a σ-compact topological space is one that can be written as a countable union of compact subsets.the generated sigma-algebra of a set is denoted the sum-of-divisors function in number theorythe Stefan–Boltzmann constantthe "sigma factor" of RNA polymerasea measure of electrical conductivitythe Surface charge density in electrostaticsNormal stress in continuum mechanicsvolatility of a stock generally needed for options pricinga syllable in phonologythe spectrum of a matrix , denoted as , in applied mathematicssurface tensionthe unary operation of selection on a database relation in relational algebrathe Pauli matrices in quantum mechanicsa target's radar cross-section (RCS) in radar jamming or Electronic Warfare (EW)the life span of a basic multicellular unit (BMU) in bone remodelingthe Damping Parameter in Signal processinga millisecond in early 20th century physiology literature.Politics
During the 1930s, an upper case Σ was in use as the symbol of the Ação Integralista Brasileira, a radical right-wing party in Brazil.
Technical notes
Unicode
There are several Unicode codepoints representing the Greek letter sigma.
The use of multiple codepoints for final / non-final sigma is somewhat unusual in Unicode. However, the two cannot always be distinguished by a simple algorithm (there are exceptions for abbreviations), and there is a significant history of them being separate characters in other specifications.
Additionally, there are at least 23 codepoints for sigma as a symbol (bold, italic, sans-serif, lunate, reversed, or dotted, in various combinations).