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Sigma

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Sigma (/ˈsɪɡmə/ SIG-mə;[1] uppercase Σ, lowercase σ, 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 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.[i][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 GREEK CAPITAL LUNATE SIGMA SYMBOL; U+03FD Ͻ GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL, U+03FE Ͼ GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL, and U+03FF Ͽ GREEK 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 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, additionally 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.

Unicode

  • U+037B ͻ GREEK SMALL REVERSED LUNATE SIGMA SYMBOL
  • U+037C ͼ GREEK SMALL DOTTED LUNATE SIGMA SYMBOL
  • U+037D ͽ GREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL
  • U+03A3 Σ GREEK CAPITAL LETTER SIGMA (Σ)
  • U+03C2 ς GREEK SMALL LETTER FINAL SIGMA (ς, ς, ς)
  • U+03C3 σ GREEK SMALL LETTER SIGMA (σ)
  • U+03F2 ϲ GREEK LUNATE SIGMA SYMBOL
  • U+03F9 Ϲ GREEK CAPITAL LUNATE SIGMA SYMBOL
  • U+03FD Ͻ GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL
  • U+03FE Ͼ GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL
  • U+03FF Ͽ GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL
  • U+2140 DOUBLE-STRUCK N-ARY SUMMATION
  • U+2211 N-ARY SUMMATION (∑, ∑)
  • U+23B2 SUMMATION TOP[a]
  • U+23B3 SUMMATION BOTTOM
  • U+2CA4 COPTIC CAPITAL LETTER SIMA
  • U+2CA5 COPTIC SMALL LETTER SIMA
  • U+2CEA COPTIC SYMBOL SHIMA SIMA
  • U+1D6BA 𝚺 MATHEMATICAL BOLD CAPITAL SIGMA[b]
  • U+1D6D3 𝛓 MATHEMATICAL BOLD SMALL FINAL SIGMA
  • U+1D6D4 𝛔 MATHEMATICAL BOLD SMALL SIGMA
  • U+1D6F4 𝛴 MATHEMATICAL ITALIC CAPITAL SIGMA
  • U+1D70D 𝜍 MATHEMATICAL ITALIC SMALL FINAL SIGMA
  • U+1D70E 𝜎 MATHEMATICAL ITALIC SMALL SIGMA
  • U+1D72E 𝜮 MATHEMATICAL BOLD ITALIC CAPITAL SIGMA
  • U+1D747 𝝇 MATHEMATICAL BOLD ITALIC SMALL FINAL SIGMA
  • U+1D748 𝝈 MATHEMATICAL BOLD ITALIC SMALL SIGMA
  • U+1D768 𝝨 MATHEMATICAL SANS-SERIF BOLD CAPITAL SIGMA
  • U+1D781 𝞁 MATHEMATICAL SANS-SERIF BOLD SMALL FINAL SIGMA
  • U+1D782 𝞂 MATHEMATICAL SANS-SERIF BOLD SMALL SIGMA
  • U+1D7A2 𝞢 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL SIGMA
  • U+1D7BB 𝞻 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL FINAL SIGMA
  • U+1D7BC 𝞼 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL SIGMA
  1. ^ Combined with U+23B3 to make a double-high sigma
  2. ^ 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.

See also

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. ^ Jump up to: a b 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.