Sigma (/ˈsɪɡmə/ SIG-mə;[1] uppercase Σ, lowercase σ, lowercase in word-final position ς; 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 𐤔 (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.[lower-roman 1][3]

According to one hypothesis,[4] the name "sigma" may continue that of Phoenician samekh (𐤎), 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 ΑΓΙΑ ΠΟΛΙϹ) uses the lunate sigma
A 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+03F9 Ϲ ; U+03FD Ͻ , U+03FE Ͼ , and U+03FF Ͽ .

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 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.

Uses

Language and linguistics

Science and mathematics

Mathematics

  • In general mathematics, lowercase σ is commonly used to represent unknown angles, as well as serving as a shorthand for "countably", whereas Σ is regularly used as the operator for summation, e.g.:

Biology, physiology, and medicine

Business, finance, and economics

Chemistry

Engineering and computer science

Physics

Organizations

  • 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.

Character encoding

Greek sigma

Character information
PreviewΣσςϹϲ
Unicode name GREEK CAPITAL LETTER SIGMA GREEK SMALL LETTER SIGMA GREEK SMALL LETTER FINAL SIGMA GREEK CAPITAL LUNATE SIGMA SYMBOL GREEK LUNATE SIGMA SYMBOL
Encodingsdecimalhexdechexdechexdechexdechex
Unicode931U+03A3963U+03C3962U+03C21017U+03F91010U+03F2
UTF-8206 163CE A3207 131CF 83207 130CF 82207 185CF B9207 178CF B2
Numeric character referenceΣΣσσςςϹϹϲϲ
Named character referenceΣσς, ς, ς
DOS Greek14591169A9170AA
DOS Greek-2207CF236EC237ED
Windows 1253211D3243F3242F2
TeX\Sigma\sigma\varsigma

[11]

Character information
PreviewϽͻϾͼϿͽ
Unicode name GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL GREEK SMALL REVERSED LUNATE SIGMA SYMBOL GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL GREEK SMALL DOTTED LUNATE SIGMA SYMBOL GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL GREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL
Encodingsdecimalhexdechexdechexdechexdechexdechex
Unicode1021U+03FD891U+037B1022U+03FE892U+037C1023U+03FF893U+037D
UTF-8207 189CF BD205 187CD BB207 190CF BE205 188CD BC207 191CF BF205 189CD BD
Numeric character referenceϽϽͻͻϾϾͼͼϿϿͽͽ

Coptic sima

Character information
PreviewⲤⲥ
Unicode name COPTIC CAPITAL LETTER SIMA COPTIC SMALL LETTER SIMA
Encodingsdecimalhexdechex
Unicode11428U+2CA411429U+2CA5
UTF-8226 178 164E2 B2 A4226 178 165E2 B2 A5
Numeric character referenceⲤⲤⲥⲥ

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.

Character information
Preview∑𝚺𝛔𝛓𝛴𝜎
Unicode name N-ARY SUMMATION MATHEMATICAL BOLD
CAPITAL SIGMA		 MATHEMATICAL BOLD
SMALL SIGMA		 MATHEMATICAL BOLD
SMALL FINAL SIGMA		 MATHEMATICAL ITALIC
CAPITAL SIGMA		 MATHEMATICAL ITALIC
SMALL SIGMA
Encodingsdecimalhexdechexdechexdechexdechexdechex
Unicode8721U+2211120506U+1D6BA120532U+1D6D4120531U+1D6D3120564U+1D6F4120590U+1D70E
UTF-8226 136 145E2 88 91240 157 154 186F0 9D 9A BA240 157 155 148F0 9D 9B 94240 157 155 147F0 9D 9B 93240 157 155 180F0 9D 9B B4240 157 156 142F0 9D 9C 8E
UTF-168721221155349 57018D835 DEBA55349 57044D835 DED455349 57043D835 DED355349 57076D835 DEF455349 57102D835 DF0E
Numeric character reference∑∑𝚺𝚺𝛔𝛔𝛓𝛓𝛴𝛴𝜎𝜎
Named character reference∑, ∑
Character information
Preview𝜍𝜮𝝈𝝇𝝨
Unicode name MATHEMATICAL ITALIC
SMALL FINAL SIGMA		 MATHEMATICAL BOLD ITALIC
CAPITAL SIGMA		 MATHEMATICAL BOLD ITALIC
SMALL SIGMA		 MATHEMATICAL BOLD ITALIC
SMALL FINAL SIGMA		 MATHEMATICAL SANS-SERIF
BOLD CAPITAL SIGMA
Encodingsdecimalhexdechexdechexdechexdechex
Unicode120589U+1D70D120622U+1D72E120648U+1D748120647U+1D747120680U+1D768
UTF-8240 157 156 141F0 9D 9C 8D240 157 156 174F0 9D 9C AE240 157 157 136F0 9D 9D 88240 157 157 135F0 9D 9D 87240 157 157 168F0 9D 9D A8
UTF-1655349 57101D835 DF0D55349 57134D835 DF2E55349 57160D835 DF4855349 57159D835 DF4755349 57192D835 DF68
Numeric character reference𝜍𝜍𝜮𝜮𝝈𝝈𝝇𝝇𝝨𝝨
Character information
Preview𝞂𝞁𝞢𝞼𝞻
Unicode name MATHEMATICAL SANS-SERIF
BOLD SMALL SIGMA		 MATHEMATICAL SANS-SERIF
BOLD SMALL FINAL SIGMA		 MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL SIGMA		 MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL SIGMA		 MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL FINAL SIGMA
Encodingsdecimalhexdechexdechexdechexdechex
Unicode120706U+1D782120705U+1D781120738U+1D7A2120764U+1D7BC120763U+1D7BB
UTF-8240 157 158 130F0 9D 9E 82240 157 158 129F0 9D 9E 81240 157 158 162F0 9D 9E A2240 157 158 188F0 9D 9E BC240 157 158 187F0 9D 9E BB
UTF-1655349 57218D835 DF8255349 57217D835 DF8155349 57250D835 DFA255349 57276D835 DFBC55349 57275D835 DFBB
Numeric character reference𝞂𝞂𝞁𝞁𝞢𝞢𝞼𝞼𝞻𝞻

See also

Wikimedia Commons has media related to the letter sigma.
Look up Σ, σ, or ς in Wiktionary, the free dictionary.

References

Notes

  1. ↑ "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)

Citations

  1. ↑ "sigma". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
  2. 1 2 Woodard, Roger D. (2006). "Alphabet". In Wilson, Nigel Guy (ed.). Encyclopedia of Ancient Greece. London: Routledge. p. 38.
  3. ↑ 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.
  4. ↑ Jeffery, Lilian H. (1961). The Local Scripts of Archaic Greece. Oxford: Clarendon. pp. 25–7.
  5. ↑ Thompson, Edward M. (1912). Introduction to Greek and Latin Paleography. Oxford: Clarendon. p. 108, 144.
  6. ↑ Hopkins, Edward C. D. (2004). "Letterform Usage | Numismatica Font Projects" Parthia.
  7. ↑ de Lisle, Christopher (2020). "Attic Inscriptions in UK Collections: Ashmolean Museum, Oxford". AIUK. 11: 11. ISSN 2054-6769. Retrieved 2 June 2022.
  8. ↑ 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.
  9. ↑ Conroy, Kevin M. (21 February 2008). "Celtic initial consonant mutations - nghath and bhfuil?" – via dlib.bc.edu.
  10. ↑ Hill, A. V. (1935). "Units and Symbols". Nature. 136 (3432): 222. Bibcode:1935Natur.136..222H. doi:10.1038/136222a0. S2CID 4087300.
  11. ↑ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)
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