|Use in other languages|
Sigma (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. When used at the end of a word (when the word is not all caps), the final form (ς) is used, e.g. Ὀδυσσεύς (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end.
- 1 History
- 2 Uses
- 2.1 Greek
- 2.2 International African Alphabet
- 2.3 Science and mathematics
- 2.4 Organizations
- 3 Character encoding
- 4 See also
- 5 References
The shape Σς and alphabetic position of sigma is derived from Phoenician shin 𐤔 . The original name of the letter 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, Ϻ. Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians.
The name "sigma", according to one hypothesis, may continue that of Phoenician Samekh, the letter continued by Greek Ξ. Alternatively, the name sigma may have been a Greek innovation that simply meant "hissing", from the root of σίζω (sízō, earlier *sig-jō, meaning "I hiss").
In handwritten Greek during the Hellenistic period (4th and 3rd centuries BC), the epigraphic form of Σ was simplified into a C-like shape. It is also found on coins from the fourth century BC onward. This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as lunate sigma (uppercase Ϲ, lowercase ϲ), because of its crescent-like shape.
It 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, encoded at U+03FE Ͼ) was used by Aristarchus of Samothrace (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an antisigma, or reversed sigma (Ͻ), may mark a line that is out of place. A dotted antisigma or dotted reversed sigma (antisigma periestigmenon: Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.
Sigma was adopted in the Old Italic alphabets beginning in the 8th century BC. A simplified three-stroke version, omitting the lowermost stroke, is found already in Western Greek alphabets, and becomes current in classical Etruscan, in Oscan, and also in the earliest Latin epigraphy (early Latin S), such as the Duenos inscription. The alternation between three and four strokes (occasionally also more than four) is 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.
International African Alphabet
Science and mathematics
Uppercase Σ is used as a symbol for:
- the summation operator
- a class of baryons in particle physics
- macroscopic cross sections in nuclear and particle physics
- self-energy in condensed matter physics
- the balance of the invoice classes and the overall amount of the debts and demands in economics
- the set of symbols that form an alphabet in linguistics and computer science
- the covariance matrix of a set of random variables in probability theory and statistics, sometimes in the form to distinguish it from the summation operator.
- The busy beaver function
Lowercase σ is used for:
Lower case sigma is used in theoretical spectral analysis as standard deviation opposed to lower case mu as the absolute mean value.
Biology and medicine
- the sigma receptor in biology
- the sigma factor of RNA polymerase
- the life span of a basic multicellular unit (BMU) in bone remodeling
- a millisecond in early 20th-century physiology literature
Business, finance, and economics
- volatility of a stock generally needed for options pricing
- the elasticity of substitution between two inputs in macroeconomics
- a quality model, Six Sigma (6σ), based on the standard deviation
Engineering and computer science
- the unary operation of selection on a database relation in relational algebra
- the Sigmoid/Logistic function in machine learning
- a target's radar cross-section (RCS) in radar jamming or electronic warfare
- the damping parameter in signal processing
Mathematics and statistics
- sigma-algebras, sigma-fields, and sigma-finiteness in measure theory; in general terms, the symbol σ serves as a shorthand for "countably", e.g. a σ-compact topological space is one that can be written as a countable union of compact subsets.
- the generated sigma-algebra of a set A is denoted σ(A)
- the sum-of-divisors function in number theory
- the spectrum of a linear map T, denoted as σ(T), in applied mathematics
- the Weierstrass sigma-function
- the standard deviation of a population or probability distribution in statistics (See Business for Six Sigma)
- an unknown angle
- cross section (physics)
- the Stefan–Boltzmann constant
- a measure of electrical conductivity
- the surface charge density in electrostatics
- normal stress in continuum mechanics
- surface tension
- the Pauli matrices in quantum mechanics
- velocity dispersion in astronomy
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.
- Greek Sigma
|Unicode name||GREEK CAPITAL LETTER SIGMA||GREEK SMALL LETTER SIGMA||GREEK SMALL LETTER FINAL SIGMA||GREEK CAPITAL LUNATE SIGMA SYMBOL||GREEK LUNATE SIGMA SYMBOL|
|UTF-8||206 163||CE A3||207 131||CF 83||207 130||CF 82||207 185||CF B9||207 178||CF B2|
|Numeric character reference||Σ||Σ||σ||σ||ς||ς||Ϲ||Ϲ||ϲ||ϲ|
|Named character reference||Σ||σ||ς|
|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|
|UTF-8||207 189||CF BD||205 187||CD BB||207 190||CF BE||205 188||CD BC||207 191||CF BF||205 189||CD BD|
|Numeric character reference||Ͻ||Ͻ||ͻ||ͻ||Ͼ||Ͼ||ͼ||ͼ||Ͽ||Ͽ||ͽ||ͽ|
- Coptic Sima
|Unicode name||COPTIC CAPITAL LETTER SIMA||COPTIC SMALL LETTER SIMA|
|UTF-8||226 178 164||E2 B2 A4||226 178 165||E2 B2 A5|
|Numeric character reference||Ⲥ||Ⲥ||ⲥ||ⲥ|
- Mathematical Sigma
|Unicode name||N-ARY SUMMATION||MATHEMATICAL BOLD
SMALL FINAL SIGMA
|UTF-8||226 136 145||E2 88 91||240 157 154 186||F0 9D 9A BA||240 157 155 148||F0 9D 9B 94||240 157 155 147||F0 9D 9B 93||240 157 155 180||F0 9D 9B B4||240 157 156 142||F0 9D 9C 8E|
|UTF-16||8721||2211||55349 57018||D835 DEBA||55349 57044||D835 DED4||55349 57043||D835 DED3||55349 57076||D835 DEF4||55349 57102||D835 DF0E|
|Numeric character reference||∑||∑||𝚺||𝚺||𝛔||𝛔||𝛓||𝛓||𝛴||𝛴||𝜎||𝜎|
|Named character reference||∑|
|Unicode name||MATHEMATICAL ITALIC
SMALL FINAL SIGMA
|MATHEMATICAL BOLD ITALIC
|MATHEMATICAL BOLD ITALIC
|MATHEMATICAL BOLD ITALIC
SMALL FINAL SIGMA
BOLD CAPITAL SIGMA
|UTF-8||240 157 156 141||F0 9D 9C 8D||240 157 156 174||F0 9D 9C AE||240 157 157 136||F0 9D 9D 88||240 157 157 135||F0 9D 9D 87||240 157 157 168||F0 9D 9D A8|
|UTF-16||55349 57101||D835 DF0D||55349 57134||D835 DF2E||55349 57160||D835 DF48||55349 57159||D835 DF47||55349 57192||D835 DF68|
|Numeric character reference||𝜍||𝜍||𝜮||𝜮||𝝈||𝝈||𝝇||𝝇||𝝨||𝝨|
|Unicode name||MATHEMATICAL SANS-SERIF
BOLD SMALL SIGMA
BOLD SMALL FINAL SIGMA
BOLD ITALIC CAPITAL SIGMA
BOLD ITALIC SMALL SIGMA
BOLD ITALIC SMALL FINAL SIGMA
|UTF-8||240 157 158 130||F0 9D 9E 82||240 157 158 129||F0 9D 9E 81||240 157 158 162||F0 9D 9E A2||240 157 158 188||F0 9D 9E BC||240 157 158 187||F0 9D 9E BB|
|UTF-16||55349 57218||D835 DF82||55349 57217||D835 DF81||55349 57250||D835 DFA2||55349 57276||D835 DFBC||55349 57275||D835 DFBB|
|Numeric character reference||𝞂||𝞂||𝞁||𝞁||𝞢||𝞢||𝞼||𝞼||𝞻||𝞻|
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.
|Wikimedia Commons has media related to the letter sigma.|
|Look up Σ, σ, or ς in Wiktionary, the free dictionary.|
- Greek letters used in mathematics, science, and engineering
- Sho (letter)
- Stigma (letter)
- Sibilant consonant
- ∑, or summation
- "Sigm-" as a combining form, as in sigmodon, sigmurethra, or in the derivative "sigmoid", as in sigmoid sinus, sigmoid colon, sigmoidoscopy, etc.
- Woodard, Roger D. (2006). "Alphabet". In Wilson, Nigel Guy (ed.). Encyclopedia of ancient Greece. London: Routldedge. p. 38.
- "…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, Histories 1.139); cf. Nick Nicholas, Non-Attic letters Archived 2012-06-28 at Archive.today.
- Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 25–27.
- Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p. 108, 144
- Parthia.com: Numismatica Font Projects.
- Hill, A. V. (1935). "Units and Symbols". Nature. 136 (3432): 222. doi:10.1038/136222a0.
- Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)