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Sigma

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Template:Short description Template:Use dmy dates Template:About Template:Pp-vandalism Template:Not to be confused with Template:Pp-vandalism Template:Greek alphabet

Sigma (Template:IPAc-en Template:Respell;<ref>Template:OED</ref> uppercase Σ, lowercase σ, lowercase in word-final position ς; Template:Langx) 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 Template:Langx (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.

HistoryEdit

The shape (Σς) and alphabetic position of sigma is derived from the Phoenician letter Template: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.<ref name="woodard">Template:Cite encyclopedia
</ref> Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians.<ref group="lower-roman">"the same letter, which the Dorians call "san", but the Ionians 'sigma'..." [translated from Ancient Greek: "Template:Langx"] (Herodotus 1.139)</ref><ref>Herodotus, Histories 1.139 — Everson, Michael and Nicholas Sims-Williams. 2002. "Non-Attic letters," transcribed by N. Nicholas. Archived from the original 2020-06-28.</ref>

According to one hypothesis,<ref name="jeffery25">Template:Cite book</ref> the name "sigma" may continue that of Phoenician samekh (Template:Phoenician letter), 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 {{#invoke:Lang|lang}} (Template:Langx, from Proto-Greek *sig-jō 'I hiss').<ref name="woodard" />

Lunate sigmaEdit

File:Madaba Jerusalem Mosaic.jpg
lang}}) uses the lunate sigma
File:Metochion Gethsimanis, Jerusalem.jpg
lang}}) 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,<ref>Thompson, Edward M. (1912). Introduction to Greek and Latin Paleography. Oxford: Clarendon. p. 108, 144.</ref> which has also been found on coins from the 4th century BC onward.<ref>Hopkins, Edward C. D. (2004). "Letterform Usage | Numismatica Font Projects" Parthia.</ref> 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).<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>

In Unicode, the above variations of lunate sigma are encoded as Template:Unichar; Template:Unichar, Template:Unichar, and Template:Unichar.

Derived alphabetsEdit

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 Latin epigraphy (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.

The letter С of Cyrillic script originates in the lunate form of Sigma.

UsesEdit

Language and linguisticsEdit

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Science and mathematicsEdit

MathematicsEdit

  • 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.:<ref name=":0">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> <math display="block">\sum_{k=0}^5k= 0 + 1 + 2 + 3 + 4 + 5 = 15</math>

  • In mathematical logic, <math>\Sigma^0_n</math> is used to denote the set of formulae with bounded quantifiers beginning with existential quantifiers, alternating <math>n-1</math> 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.
  • In statistics, σ represents the standard deviation of population or probability distribution (where mu or μ is used for the mean).<ref name=":0" />
  • In topology, σ-compact topological space is one that can be written as a countable union of compact subsets.<ref>{{#invoke:citation/CS1|citation

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Biology, physiology, and medicineEdit

Business, finance, and economicsEdit

ChemistryEdit

Engineering and computer scienceEdit

PhysicsEdit

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OrganizationsEdit

  • 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.

UnicodeEdit

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See alsoEdit

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ReferencesEdit

NotesEdit

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CitationsEdit

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