Sigma (/ˈsɪɡmə/SIG-mə;[1]uppercaseΣ, lowercaseσ, lowercase in word-final position ς; Ancient Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (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. The Latin letter S derives from sigma while the Cyrillic letter Es derives from a lunate form of this letter.
History
The shape (Σς) and alphabetic position of sigma is derived from the Phoenician letter (shin).
Sigma's original name 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 in the Greek alphabet, represented as Ϻ.[2]Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians.[i][3]
According to one hypothesis,[4] the name "sigma" may continue that of Phoenician samekh (), the letter continued through Greek xi, represented as Ξ. Alternatively, the name may have been a Greek innovation that simply meant 'hissing', from the root of σίζω (sízō, from Proto-Greek*sig-jō 'I hiss').[2]
Lunate sigma
The Madaba Map, a sixth-century mosaic of Jerusalem (Η ΑΓΙΑΠΟΛΙϹ) uses the lunate sigmaA plaque reading "Metochion of Gethsemane" (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–3rd century BC), the epigraphic 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 as lunate sigma (uppercase Ϲ, lowercase ϲ), because of its crescent-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 by Aristarchus 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]
In Unicode, the above variations of lunate sigma are encoded as U+03F9ϹGREEK CAPITAL LUNATE SIGMA SYMBOL;
U+03FDϽGREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL,
U+03FEϾGREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL, and
U+03FFϿGREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL.
Derived alphabets
Sigma was adopted in the Old 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 classical Etruscan and Oscan, as well as in the earliest Latinepigraphy (early Latin S), such as the Duenos inscription.
The alternation between three and four (and occasionally more than four) strokes was also adopted into the early runic alphabet (early form of the s-rune).
Both the Anglo-Saxon runes and the Younger Futhark consistently use the simplified three-stroke version.
In general mathematics, lowercase σ is commonly used to represent unknown angles, additionally serving as a shorthand for "countably", whereas Σ is regularly used as the operator for summation, e.g.:
In mathematical 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 the arithmetic 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
^The MATHEMATICAL 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.
^"the same letter, which the Dorians call "san", but the Ionians 'sigma'..." [translated from Ancient Greek: "τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα"] (Herodotus 1.139)
^Follet, Simone (2000). "Les deux archontes Pamménès du Ier siècle a.c. à Athènes". Revue des Études Grecques. 113: 188–192. doi:10.3406/reg.2000.4402.
