Sigma (/ˈsɪɡmə/SIG-mə;[1]uppercaseΣ,lowercaseσ, lowercase in word-final positionς;Ancient Greek:σίγμα) is the eighteenth letter of theGreek alphabet. In the system ofGreek numerals, it has a value of 200. In general mathematics, uppercaseΣ is used as anoperator forsummation. When used at the end of aletter-case word (one that does not useall caps), thefinal form (ς) is used. InὈδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. TheLatin letterS derives from sigma while theCyrillic letterEs derives from alunate form of this letter.
History
The shape (Σς) and alphabetic position of sigma is derived from thePhoenician letter (shin).
Sigma's original name may have beensan, but due to the complicated early history of the Greekepichoric alphabets,san came to be identified as a separate letter in the Greek alphabet, represented asϺ.[2]Herodotus reports that "san" was the name given by theDorians to the same letter called "sigma" by theIonians.[i][3]
According to one hypothesis,[4] the name "sigma" may continue that of Phoeniciansamekh (), the letter continued through Greekxi, represented asΞ. Alternatively, the name may have been a Greek innovation that simply meant 'hissing', from the root ofσίζω (sízō, fromProto-Greek*sig-jō 'I hiss').[2]
Lunate sigma
TheMadaba Map, a sixth-century mosaic ofJerusalem (ΗΑΓΙΑΠΟΛΙϹ) uses the lunate sigmaA plaque reading "Metochion ofGethsemane" (Μετόχιον Γεθσημανῆς) in Jerusalem, with a lunate sigma both at the end and in the middle of the word
In handwritten Greek during theHellenistic period (4th–3rd century BC), theepigraphic form of Σ was simplified into a C-like shape,[5] which has also been found on coins from the 4th century BC onward.[6] This became the universal standard form of sigma during late antiquity and the Middle Ages.
Today, it is known aslunate sigma (uppercaseϹ, lowercaseϲ), because of itscrescent-like shape, and 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,Ͼ) was used byAristarchus of Samothrace (220–143 BC) as an editorial sign indicating that the line marked as such is at an incorrect position. Similarly, a reversed sigma (antisigma,Ͻ), may mark a line that is out of place. A dotted antisigma (antisigma periestigmenon,Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.
In Greek inscriptions from the late first century BC onwards,Ͻ was an abbreviation indicating that a man's father's name is the same as his own name, thus Dionysodoros son of Dionysodoros would be written Διονυσόδωρος Ͻ (Dionysodoros Dionysodorou).[7][8]
InUnicode, the above variations of lunate sigma are encoded asU+03F9ϹGREEK CAPITAL LUNATE SIGMA SYMBOL;U+03FDϽGREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL,U+03FEϾGREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL, andU+03FFϿGREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL.
Derived alphabets
Sigma was adopted in theOld Italic alphabets beginning in the 8th century BC.At that time a simplified three-stroke version, omitting the lowermost stroke, was already found in Western Greek alphabets,and was incorporated into classicalEtruscan andOscan, as well as in the earliestLatinepigraphy (early LatinS), such as theDuenos inscription.The alternation between three and four (and occasionally more than four) strokes was also adopted into theearly runic alphabet (early form of thes-rune).Both theAnglo-Saxon runes and theYounger Futhark consistently use the simplified three-stroke version.
In general mathematics, lowercaseσ is commonly used to represent unknown angles, additionally serving as a shorthand for "countably", whereasΣ is regularly used as theoperator forsummation, e.g.:[10]
Inmathematical logic, is used to denote the set of formulae with bounded quantifiers beginning with existential quantifiers, alternating times between existential and universal quantifiers. This notation reflects an indirect analogy between the relationship of summation and products on one hand, and existential and universal quantifiers on the other. See the article on thearithmetic hierarchy.
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.
Unicode
U+037BͻGREEK SMALL REVERSED LUNATE SIGMA SYMBOL
U+037CͼGREEK SMALL DOTTED LUNATE SIGMA SYMBOL
U+037DͽGREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL
U+03A3ΣGREEK CAPITAL LETTER SIGMA (Σ)
U+03C2ςGREEK SMALL LETTER FINAL SIGMA (ς, ς, ς)
U+03C3σGREEK SMALL LETTER SIGMA (σ)
U+03F2ϲGREEK LUNATE SIGMA SYMBOL
U+03F9ϹGREEK CAPITAL LUNATE SIGMA SYMBOL
U+03FDϽGREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL
U+03FEϾGREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL
U+03FFϿGREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL
^TheMATHEMATICAL characters should only be used for math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
