Sigma (;
uppercase
Letter case is the distinction between the Letter (alphabet), letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain lang ...
Σ,
lowercase
Letter case is the distinction between the Letter (alphabet), letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain lang ...
σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the
Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as we ...
. In the system of
Greek numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to tho ...
, it has a value of 200. In general mathematics, uppercase Σ is used as an
operator for
summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, mat ...
. When used at the end of a
letter-case word (one that does not use
all caps
In typography, all caps (short for "all capitals") refers to text or a font in which all letters are capital letters, for example: "THIS TEXT IS IN ALL CAPS". All caps may be used for emphasis (for a word or phrase). They are commonly seen in ...
), 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
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
letter
S derives from sigma while the
Cyrillic
, bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця
, fam1 = Egyptian hieroglyphs
, fam2 = Proto-Sinaitic
, fam3 = Phoenician
, fam4 = G ...
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
(
''shin'').
Sigma's original name may have been ''san'', but due to the complicated early history of the Greek
epichoric alphabets
Many local variants of the Greek alphabet were employed in ancient Greece during the archaic and early classical periods, until around 400 BC, when they were replaced by the classical 24-letter alphabet that is the standard today. All forms ...
, ''san'' came to be identified as a separate letter in the Greek alphabet, represented as
Ϻ.
Herodotus
Herodotus ( ; grc, , }; BC) was an ancient Greek historian and geographer from the Greek city of Halicarnassus, part of the Persian Empire (now Bodrum, Turkey) and a later citizen of Thurii in modern Calabria ( Italy). He is known f ...
reports that "san" was the name given by the
Dorians
The Dorians (; el, Δωριεῖς, ''Dōrieîs'', singular , ''Dōrieús'') were one of the four major ethnic groups into which the Hellenes (or Greeks) of Classical Greece divided themselves (along with the Aeolians, Achaeans, and Ionians) ...
to the same letter called "sigma" by the
Ionians
The Ionians (; el, Ἴωνες, ''Íōnes'', singular , ''Íōn'') were one of the four major tribes that the Greeks considered themselves to be divided into during the ancient period; the other three being the Dorians, Aeolians, and Achae ...
.
["the same letter, which the Dorians call "san", but the Ionians 'sigma'..." ranslated_from_Ancient_Greek:_"".html" ;"title="Ancient_Greek.html" ;"title="ranslated from Ancient Greek">ranslated from Ancient Greek: """>Ancient_Greek.html" ;"title="ranslated from Ancient Greek">ranslated from Ancient Greek: ""(]Herodotus
Herodotus ( ; grc, , }; BC) was an ancient Greek historian and geographer from the Greek city of Halicarnassus, part of the Persian Empire (now Bodrum, Turkey) and a later citizen of Thurii in modern Calabria ( Italy). He is known f ...
1.139)
According to one hypothesis,
the name "sigma" may continue that of Phoenician ''samekh'' (
), the letter continued through Greek ''xi'', represented as Xi (letter), Ξ. Alternatively, the name may have been a Greek innovation that simply meant 'hissing', from the root of (, from
Proto-Greek
The Proto-Greek language (also known as Proto-Hellenic) is the Indo-European language which was the last common ancestor of all varieties of Greek, including Mycenaean Greek, the subsequent ancient Greek dialects (i.e., Attic, Ionic, Ae ...
''*sig-jō'' 'I hiss').
Lunate sigma
![Metochion Gethsimanis, Jerusalem](https://upload.wikimedia.org/wikipedia/commons/1/1f/Metochion_Gethsimanis%2C_Jerusalem.jpg)
In handwritten Greek during the
Hellenistic period
In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in 3 ...
(4th–3rd century BC), the
epigraphic
Epigraphy () is the study of inscriptions, or epigraphs, as writing; it is the science of identifying graphemes, clarifying their meanings, classifying their uses according to dates and cultural contexts, and drawing conclusions about the wr ...
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
A crescent shape (, ) is a symbol or emblem used to represent the lunar phase in the first quarter (the "sickle moon"), or by extension a symbol representing the Moon itself.
In Hinduism, Lord Shiva is often shown wearing a crescent moon on his ...
-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
Aristarchus of Samothrace ( grc-gre, Ἀρίσταρχος ὁ Σαμόθραξ ''Aristarchos o Samothrax''; c. 220 – c. 143 BC) was an ancient Greek grammarian, noted as the most influential of all scholars of Homeric poetry. He was the h ...
(220–143 BC) as an editorial sign indicating that the line marked as such is at an incorrect position. Similarly, a reversed sigma (''
antisigma
The Claudian letters were developed by the Roman emperor Claudius (reigned 41–54). He introduced three new letters to the Latin alphabet:
*Ↄ or ↃϹ/X (''antisigma'') to replace BS and PS, much as X stood in for CS and GS. The shape ...
'', 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'').
In
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ...
, the above variations of lunate sigma are encoded as ;
,
, and
.
Derived alphabets
Sigma was adopted in the
Old Italic alphabets
The Old Italic scripts are a family of similar ancient writing systems used in the Italy, Italian Peninsula between about 700 and 100 BC, for various languages spoken in that time and place. The most notable member is the Etruscan alphabet, ...
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 __NOTOC__
Etruscan may refer to:
Ancient civilization
*The Etruscan language, an extinct language in ancient Italy
*Something derived from or related to the Etruscan civilization
**Etruscan architecture
**Etruscan art
**Etruscan cities
** Etrusca ...
and
Oscan
Oscan is an extinct Indo-European language of southern Italy. The language is in the Osco-Umbrian or Sabellic branch of the Italic languages. Oscan is therefore a close relative of Umbrian.
Oscan was spoken by a number of tribes, including th ...
, as well as in the earliest
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
epigraphy
Epigraphy () is the study of inscriptions, or epigraphs, as writing; it is the science of identifying graphemes, clarifying their meanings, classifying their uses according to dates and cultural contexts, and drawing conclusions about the wr ...
(early Latin ''
S''), such as the
Duenos inscription
The Duenos inscription is one of the earliest known Old Latin texts, variously dated from the 7th to the 5th century BC. It is inscribed on the sides of a '' kernos'', in this case a trio of small globular vases adjoined by three clay struts. It ...
.
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
Anglo-Saxon runes ( ang, rūna ᚱᚢᚾᚪ) are runes used by the early Anglo-Saxons as an alphabet in their writing system. The characters are known collectively as the futhorc (ᚠᚢᚦᚩᚱᚳ ''fuþorc'') from the Old English sound va ...
and the
Younger Futhark
The Younger Futhark, also called Scandinavian runes, is a runic alphabet and a reduced form of the Elder Futhark, with only 16 characters, in use from about the 9th century, after a "transitional period" during the 7th and 8th centuries.
The r ...
consistently use the simplified three-stroke version.
The letter
С of
Cyrillic script
The Cyrillic script ( ), Slavonic script or the Slavic script, is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic languages, Slavic, Turkic languages, Turkic, Mongolic languages, ...
originates in the
lunate form of Sigma.
Uses
Language and linguistics
* In both
Ancient
Ancient history is a time period from the History of writing, beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian language, Sumerian c ...
and
Modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...
, the sigma represents the
voiceless alveolar fricative
The voiceless alveolar fricatives are a type of fricative consonant pronounced with the tip or blade of the tongue against the alveolar ridge (gum line) just behind the teeth. This refers to a class of sounds, not a single sound. There are at least ...
. In Modern Greek, this sound is
voiced
Voice or voicing is a term used in phonetics and phonology to characterize speech sounds (usually consonants). Speech sounds can be described as either voiceless (otherwise known as ''unvoiced'') or voiced.
The term, however, is used to refer ...
to the
voiced alveolar fricative
The voiced alveolar fricatives are consonantal sounds. The symbol in the International Phonetic Alphabet that represents these sounds depends on whether a sibilant or non-sibilant fricative is being described.
* The symbol for the alveolar sibilant ...
when occurring before , , , or .
* The uppercase form of sigma (Σ) was re-borrowed into the
Latin alphabet
The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write English and the o ...
—more precisely, the
International African Alphabet—to serve as the uppercase of modern
''esh'' (lowercase: ʃ).
* In
phonology
Phonology is the branch of linguistics that studies how languages or dialects systematically organize their sounds or, for sign languages, their constituent parts of signs. The term can also refer specifically to the sound or sign system of a ...
, σ is used to represent
syllables
A syllable is a unit of organization for a sequence of speech sounds typically made up of a syllable nucleus (most often a vowel) with optional initial and final margins (typically, consonants). Syllables are often considered the phonological "bu ...
.
* In
linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
, Σ represents the set of symbols that form an alphabet (see also
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
).
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
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers; ...
", whereas Σ is regularly used as the
operator for
summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, mat ...
, e.g.:
**
*In
mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
,
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
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on the complexity of formulas that define t ...
.
*In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, σ represents the
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
of population or
probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
(where
mu or μ is used for the mean).
*In
topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
, σ-compact
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...
is one that can be written as a countable
union
Union commonly refers to:
* Trade union, an organization of workers
* Union (set theory), in mathematics, a fundamental operation on sets
Union may also refer to:
Arts and entertainment
Music
* Union (band), an American rock group
** ''Un ...
of
compact subsets.
*In
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
and in
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
, there is a type of
algebra of sets
In mathematics, the algebra of sets, not to be confused with the mathematical structure of ''an'' algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the ...
known as
σ-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set ''X'' is a collection Σ of subsets of ''X'' that includes the empty subset, is closed under complement, and is closed under countable unions and countabl ...
(aka σ-field). Sigma algebra also includes terms such as:
**σ(''A''), denoting the
generated sigma-algebra of a set ''A''
**
σ-finite measure (see
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...
)
* In
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
, σ is included in various
divisor functions, especially the sigma function or sum-of-divisors function.
* In
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
, σ(''T'') denotes the spectrum of a
linear map
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a Map (mathematics), mapping V \to W between two vect ...
''T''.
* In
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
, σ is used in the
Weierstrass sigma-function.
*In
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
and
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, Σ denotes the
covariance matrix
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of ...
of a set of
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
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
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
, the
sigma receptor
Sigma receptors (σ-receptors) are protein cell surface receptors that bind ligands such as 4-PPBP (4-phenyl-1-(4-phenylbutyl) piperidine), SA 4503 (cutamesine), ditolylguanidine, dimethyltryptamine, and siramesine. There are two subtypes, ...
(σ–receptors) is a type of
cell surface receptor
Cell surface receptors (membrane receptors, transmembrane receptors) are receptors that are embedded in the plasma membrane of cells. They act in cell signaling by receiving (binding to) extracellular molecules. They are specialized integral m ...
.
* In
biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, the
σ factor (or specificity factor) is a protein found in
RNA polymerase
In molecular biology, RNA polymerase (abbreviated RNAP or RNApol), or more specifically DNA-directed/dependent RNA polymerase (DdRP), is an enzyme that synthesizes RNA from a DNA template.
Using the enzyme helicase, RNAP locally opens the ...
.
* In
bone physiology, the
bone remodeling period In bone physiology, the bone remodeling period describes the temporal duration (i.e. lifespan) of the basic multicellular unit (BMU) that is responsible for bone turnover. Historically, this was referred to as the sigma (σ) or sigma period, but t ...
—i.e., the
life span of a basic multicellular unit—has historically been referred to as the sigma period
* In early 20th-century
physiology
Physiology (; ) is the scientific study of functions and mechanisms in a living system. As a sub-discipline of biology, physiology focuses on how organisms, organ systems, individual organs, cells, and biomolecules carry out the chemical ...
literature, σ had been used to represent
milliseconds
A millisecond (from ''milli-'' and second; symbol: ms) is a unit of time in the International System of Units (SI) equal to one thousandth (0.001 or 10−3 or 1/1000) of a second and to 1000 microseconds.
A unit of 10 milliseconds may be called ...
Business, finance, and economics
* In
finance
Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...
, σ is the symbol used to represent
volatility of
stocks
Stocks are feet restraining devices that were used as a form of corporal punishment and public humiliation. The use of stocks is seen as early as Ancient Greece, where they are described as being in use in Solon's law code. The law describing ...
, usually measured by the
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
of
logarithmic returns.
*In
accounting
Accounting, also known as accountancy, is the measurement, processing, and communication of financial and non financial information about economic entities such as businesses and corporations. Accounting, which has been called the "languag ...
, Σ indicates the
balance
Balance or balancing may refer to:
Common meanings
* Balance (ability) in biomechanics
* Balance (accounting)
* Balance or weighing scale
* Balance as in equality or equilibrium
Arts and entertainment Film
* ''Balance'' (1983 film), a Bulgaria ...
of invoice classes and the overall amount of debts and demands.
* In
macroeconomics
Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole.
For example, using interest rates, taxes, and ...
, σ is used in equations to represent the
elasticity of substitution Elasticity of substitution is the ratio of percentage change in capital-labour ratio with the percentage change in Marginal Rate of Technical Substitution. In a competitive market, it measures the percentage change in the two inputs used in respons ...
between two inputs.
* In the
machine industry
The machine industry or machinery industry is a subsector of the industry, that produces and maintains machines for consumers, the industry, and most other companies in the economy.
This machine industry traditionally belongs to the heavy indust ...
,
Six Sigma (6σ) is a quality model based on the
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
.
Chemistry
*
Sigma bond
In chemistry, sigma bonds (σ bonds) are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most simply defined for diatomic molecules using the language and tools of s ...
s (σ bonds) are the strongest type of
covalent
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
chemical bond
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
.
* In
organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
, σ symbolizes the sigma constant of
Hammett equation
The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with ju ...
.
* In
alchemy
Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Greek: χυμεία, ''khumeía'') is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practiced in China, India, the Muslim world, ...
, Σ was sometimes used to represent
sugar
Sugar is the generic name for sweet-tasting, soluble carbohydrates, many of which are used in food. Simple sugars, also called monosaccharides, include glucose, fructose, and galactose. Compound sugars, also called disaccharides or double ...
.
Engineering and computer science
* In
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, Σ represents the set of symbols that form an alphabet (see also
linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
)
*
Relational algebra
In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. The theory was introduced by Edgar F. Codd.
The main application of relational algebra ...
uses the values
and
to denote
selections, which are a type of
unary operation
In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function , where is a set. The function is a unary operation on ...
.
* In
machine learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence.
Machine ...
, σ is used in the formula that derives the
Sigmoid function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula:
:S(x) = \frac = \f ...
.
* In
radar jamming
Radar jamming and deception is a form of electronic countermeasures that intentionally sends out radio frequency signals to interfere with the operation of radar by saturating its receiver with noise or false information. Concepts that blanket the ...
or
electronic warfare
Electronic warfare (EW) is any action involving the use of the electromagnetic spectrum (EM spectrum) or directed energy to control the spectrum, attack an enemy, or impede enemy assaults. The purpose of electronic warfare is to deny the opponen ...
,
radar cross-sections (RCS) are commonly represented as σ when measuring the size of a target's image on radar.
* In
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...
, σ denotes the
damping ratio
Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
of a system parameter.
*In
theoretical computer science
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory.
It is difficult to circumsc ...
, Σ serves as the
busy beaver function.
*In
civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...
, σ refers to the normal stress applied on a material or structure.
Physics
* In
nuclear
Nuclear may refer to:
Physics
Relating to the nucleus of the atom:
* Nuclear engineering
*Nuclear physics
*Nuclear power
*Nuclear reactor
*Nuclear weapon
*Nuclear medicine
*Radiation therapy
*Nuclear warfare
Mathematics
*Nuclear space
*Nuclear ...
and
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, σ is used to denote
cross sections in general (see also
RCS
RCS may refer to:
Organisations
*Racing Club de Strasbourg Alsace
* Radio Corporation of Singapore
*Radcliffe Choral Society
* Rawmarsh Community School
*Red Crescent Society
*Red Cross Society
* Representation of Czechs and Slovaks, a football t ...
), while Σ represents macroscopic
cross section
Cross section may refer to:
* Cross section (geometry)
** Cross-sectional views in architecture & engineering 3D
*Cross section (geology)
* Cross section (electronics)
* Radar cross section, measure of detectability
* Cross section (physics)
**Abs ...
s
/length
* The symbol is to denote the
Stefan–Boltzmann constant
The Stefan–Boltzmann constant (also Stefan's constant), a physical constant denoted by the Greek letter ''σ'' (sigma), is the constant of proportionality in the Stefan–Boltzmann law: "the total intensity radiated over all wavelengths inc ...
.
* In relation to fundamental properties of material, σ is often used to signify
electrical conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
.
* In
electrostatics
Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...
, σ represents
surface charge
Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge di ...
density.
* In
continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...
, σ is used to signify
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
.
* In
condensed matter physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the sub ...
, Σ denotes
self-energy
In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between ...
.
* The symbol can be used to signify
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...
(alternatively, ''
γ'' or ''
T'' are also used instead).
* In
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, σ is used to indicate
Pauli matrices
In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () when used in ...
.
* In
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, σ represents
velocity dispersion
In astronomy, the velocity dispersion (''σ'') is the statistical dispersion of velocity, velocities about the Arithmetic mean, mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or ...
.
* In astronomy, the prefix Σ is used to designate double stars of the
Catalogus Novus Stellarum Duplicium by
Friedrich Georg Wilhelm von Struve
Friedrich Georg Wilhelm von Struve (russian: link=no, Василий Яковлевич Струве, trans. ''Vasily Yakovlevich Struve''; 15 April 1793 – ) was a Baltic German astronomer and geodesist from the famous Struve family. He is bes ...
.
* In particle physics, Σ represents a class of
baryon
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
s.
Organizations
* During the 1930s, an uppercase Σ was in use as the symbol of the
Ação Integralista Brasileira, a fascist political party in
Brazil
Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...
.
*
Sigma Corporation
is a Japanese company, manufacturing cameras, lenses, flashes and other photographic accessories. All Sigma products are produced in the company's own Aizu factory in Bandai, Fukushima, Japan. Although Sigma produces several camera models, ...
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
Sigma-Aldrich (formally MilliporeSigma) is an American chemical, life science, and biotechnology company that is owned by the German chemical conglomerate Merck Group.
Sigma-Aldrich was created in 1975 by the merger of Sigma Chemical Company a ...
incorporate both the name and the character in their logo.
Character encoding
Greek sigma
[Unicode Code Charts]
Greek and Coptic (Range: 0370-03FF)
/ref>
Coptic sima
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.
See also
*Antisigma
The Claudian letters were developed by the Roman emperor Claudius (reigned 41–54). He introduced three new letters to the Latin alphabet:
*Ↄ or ↃϹ/X (''antisigma'') to replace BS and PS, much as X stood in for CS and GS. The shape ...
*Greek letters used in mathematics, science, and engineering
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these cont ...
*Sampi
Sampi (modern: ϡ; ancient shapes: , ) is an archaic letter of the Greek alphabet. It was used as an addition to the classical 24-letter alphabet in some eastern Ionic dialects of ancient Greek in the 6th and 5th centuries BC, to denote some t ...
*Sho (letter)
The letter (sometimes called sho or san) was a letter added to the Greek alphabet in order to write the Bactrian language.Everson, M. and Sims-Williams, N. (2002) Proposal to add two Greek letters for Bactrian to the UCS,ISO/IEC JTC1/SC2/ ...
* Stigma (letter)
*Sibilant consonant
Sibilants are fricative consonants of higher amplitude and Fundamental frequency, pitch, made by manner of articulation, directing a stream of air with the tongue towards the teeth. Examples of sibilants are the consonants at the beginning of the ...
*Summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, mat ...
(Σ)
*Combining form "''sigm-''" (e.g. ''sigmodon'', ''sigmurethra'', etc.)
*Derivative "''sigmoid
Sigmoid means resembling the lower-case Greek letter sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς) or the Latin letter S. Specific uses include:
* Sigmoid function, a mathematical function
* Sigmoid colon, part of the l ...
''" (e.g. sigmoid sinus
The sigmoid sinuses (sigma- or s-shaped hollow curve), also known as the , are venous sinuses within the skull that receive blood from posterior dural venous sinus veins.
Structure
The sigmoid sinus is a dural venous sinus situated within the du ...
, sigmoid colon
The sigmoid colon (or pelvic colon) is the part of the large intestine that is closest to the rectum and anus. It forms a loop that averages about in length. The loop is typically shaped like a Greek letter sigma (ς) or Latin letter S (thus ''s ...
, sigmoidoscopy
Sigmoidoscopy (from the Greek term for letter " s/ς" + "eidos" + "scopy": namely, to look inside an "s"/"ς"-like object) is the minimally invasive medical examination of the large intestine from the rectum through to the nearest part of the co ...
, etc.)
References
Notes
Citations
{{Reflist
Greek letters
Letters with final form