σ, lowercase in word-final position ς; grc-gre|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 ∑ is used as an operator
. When used at the end of a letter-case
word (one that does not use all caps
), the final form
(ς) is used. In ' (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 shape (Σς) and alphabetic position of sigma is derived from the Phoenician
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
reports that "san" was the name given by the Dorians
to the same letter called "sigma" by the Ionians
["the same letter, which the Dorians call "san", but the Ionians 'sigma'…" ranslated_from_[[Ancient_Greek:_"".html" style="text-decoration: none;"class="mw-redirect" title="Ancient_Greek.html" style="text-decoration: none;"class="mw-redirect" title="ranslated from [[Ancient Greek">ranslated from [[Ancient Greek: """>Ancient_Greek.html" style="text-decoration: none;"class="mw-redirect" title="ranslated from [[Ancient Greek">ranslated from [[Ancient Greek: ""([[Herodotus 1.139)]
According to one hypothesis,
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 (, from Proto-Greek
''*sig-jō'' 'I hiss').
In handwritten Greek during the Hellenistic period
(4th–3rd century BC), the epigraphic
form of Σ was simplified into a C-like shape, which has also been found on coins from the 4th century BC onward. 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.
, the above variations of lunate sigma are encoded as ;
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
and in 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 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.
The forms of the Coptic letter
''sima'' (; 2nd century BC) and
of Cyrillic letter
'' (С; 9th century AD) are derived from lunate sigma.
Language and linguistics
* In both Ancient
and Modern Greek
, the sigma represents the voiceless alveolar fricative
. In Modern Greek, this sound is voiced
to before , , , or .
* The uppercase form of sigma (Σ) was re-borrowed into the Latin alphabet
—more precisely, the International African Alphabet
—to serve as the uppercase of modern ''esh''
* In phonology
, σ is used to represent syllables
* In linguistics
, Σ represents the set of symbols that form an alphabet (see also computer science
Science and mathematics
* In general mathematics, lowercase σ is commonly used to represent unknown angles, as well as serving as a shorthand for "countably
", whereas ∑ is regularly used as the operator
*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
, σ represents the standard deviation
of population or probability distribution
or μ is used for the mean).
, σ-compact topological space
is one that can be written as a countable union
of compact subsets
*In mathematical analysis
and in probability theory
, there is a type of algebra of sets
known as σ-algebra
(aka σ-field). Sigma algebra also includes terms such as:
**σ(''A''), denoting the generated sigma-algebra
of a set ''A''
(see measure theory
* In number theory
, σ is included in various divisor functions
, especially the sigma function or sum-of-divisors function.
* In applied mathematics
, σ(''T'') denotes the spectrum of a linear map
* In complex analysis
, σ is used in the Weierstrass sigma-function
*In probability theory
, Σ denotes the covariance matrix
of a set of random variable
s, sometimes in the form
to distinguish it from the summation operator.
*Theoretical spectral analysis
uses σ as standard deviation opposed to lowercase mu
as the absolute mean value.
Biology, physiology, and medicine
* In biology
, the sigma receptor
(σ–receptors) is a type of cell surface receptor
* In biochemistry
, the σ factor
(or specificity factor) is a protein found in RNA polymerase
* In bone physiology
, the bone remodeling period
—i.e., the life span
of a basic multicellular unit—has historically been referred to as the sigma period
* In early 20th-century physiology
literature, σ had been used to represent milliseconds
Business, finance, and economics
* In finance
, σ is the symbol used to represent volatility
, usually measured by the standard deviation
of logarithmic returns
, Σ indicates the balance
of invoice classes and the overall amount of debts and demands.
* In macroeconomics
, σ is used in equations to represent the elasticity of substitution
between two inputs.
* In the machine industry
, Six Sigma
(6σ) is a quality model based on the standard deviation
* Sigma bond
s (σ bonds) are the strongest type of covalent chemical bond
* In organic chemistry
, σ symbolizes the sigma constant of Hammett equation
* In alchemy
, Σ was sometimes used to represent sugar
Engineering and computer science
* In computer science
, Σ represents the set of symbols that form an alphabet (see also linguistics
uses the values
to denote selections
, which are a type of unary operation
* In machine learning
, σ is used in the formula that derives the Sigmoid function
* In radar jamming
or electronic warfare
, radar cross-sections
(RCS) are commonly represented as σ when measuring the size of a target's image on radar.
* In signal processing
, σ denotes the damping ratio
of a system parameter.
*In theoretical computer science
, Σ serves as the busy beaver
* In nuclear
and particle physics
, σ is used to denote cross sections
in general(see also RCS
), while Σ represents macroscopic cross section
* The symbol is to denote the Stefan–Boltzmann constant
* In relation to fundamental properties of material, σ is often used to signify electrical conductivity
* In electrostatics
, σ represents surface charge
* in continuum mechanics
, σ is used to signify stress
*In condensed matter physics
, Σ denotes self-energy
* The symbol can be used to signify surface tension
'' or ''T
'' are also used instead).
* In quantum mechanics
, σ is used to indicate Pauli matrices
* In astronomy
, σ represents velocity dispersion
*In particle physics, Σ represents a class of baryon
* 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 Code Charts]
Greek and Coptic (Range: 0370-03FF)
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.
*Greek letters used in mathematics, science, and engineering
* − Template to produce the character
*Combining form "''sigm-''" (e.g. ''sigmodon'', ''sigmurethra'', etc.)
*Derivative "''sigmoid''" (e.g. sigmoid sinus, sigmoid colon, sigmoidoscopy, etc.)
Category:Letters with final form