Delta (; uppercase Δ, lowercase δ or 𝛿; el, δέλτα, ''délta'', ) is the fourth 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 4. It was derived from the
Phoenician letter dalet
Dalet (, also spelled Daleth or Daled) is the fourth letter of the Semitic abjads, including Phoenician Dālet 𐤃, Hebrew Dālet , Aramaic Dālath , Syriac Dālaṯ , and Arabic (in abjadi order; 8th in modern order). Its sound value is t ...
𐤃. Letters that come from delta include
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 ...
D and
Cyrillic
, bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця
, fam1 = Egyptian hieroglyphs
, fam2 = Proto-Sinaitic
, fam3 = Phoenician
, fam4 = G ...
Д.
A
river delta
A river delta is a landform shaped like a triangle, created by deposition (geology), deposition of sediment that is carried by a river and enters slower-moving or stagnant water. This occurs where a river enters an ocean, sea, estuary, lake, res ...
(originally, the
delta
Delta commonly refers to:
* Delta (letter) (Δ or δ), a letter of the Greek alphabet
* River delta, at a river mouth
* D ( NATO phonetic alphabet: "Delta")
* Delta Air Lines, US
* Delta variant of SARS-CoV-2 that causes COVID-19
Delta may also ...
of the
Nile River
The Nile, , Bohairic , lg, Kiira , Nobiin: Áman Dawū is a major north-flowing river in northeastern Africa. It flows into the Mediterranean Sea. The Nile is the longest river in Africa and has historically been considered the longest rive ...
) is so named because its shape approximates the triangular uppercase letter delta. Contrary to a popular legend, this use of the word ''delta'' was not coined by
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 ...
.
Pronunciation
In
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
, delta represented a
voiced dental plosive
The voiced alveolar, dental and postalveolar plosives (or stops) are types of consonantal sounds used in many spoken languages. The symbol in the International Phonetic Alphabet that represents voiced dental, alveolar, and postalveolar plosiv ...
. In
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 ...
, it represents a
voiced dental fricative
The voiced dental fricative is a consonant sound used in some spoken languages. It is familiar to English-speakers as the ''th'' sound in ''father''. Its symbol in the International Phonetic Alphabet is eth, or and was taken from the Old Engli ...
, like the "th" in "that" or "this" (while in foreign words is instead commonly transcribed as ντ). Delta is
romanized
Romanization or romanisation, in linguistics, is the conversion of text from a different writing system to the Roman (Latin) script, or a system for doing so. Methods of romanization include transliteration, for representing written text, and ...
as ''d'' or ''dh''.
Uppercase
The uppercase letter Δ is used to denote:
* Change of any changeable quantity, in mathematics and the sciences (more specifically, the
difference operator
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
[online copy](_blank)
/ref>); for example, in:the average change of y per unit x (i.e. the change of y over the change of x). Delta is the initial letter of the Greek word διαφορά ''diaphorá'', "difference". (The small 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 d is used in much the same way for the notation of derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...
s and differentials, which also describe change by infinitesimal
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referr ...
amounts.)
* The Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the ...
:
*:
* The discriminant
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the origi ...
of a polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...
equation, especially the quadratic equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as
ax^2 + bx + c = 0\,,
where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equati ...
:
*:
* The area of a triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non-collinear ...
*:
* The symmetric difference
In mathematics, the symmetric difference of two sets, also known as the disjunctive union, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets \ and \ is \.
Th ...
of two sets
* A macroscopic change in the value of a variable in mathematics or science
* Uncertainty
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or ...
in a physical variable as seen in the uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
* An interval of possible values for a given quantity
* Any of the delta particles in particle physics
* The determinant of the matrix of coefficients of a set of linear equations (see Cramer's rule
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants o ...
)
* That an associated locant
In the nomenclature of organic chemistry, a locant is a term to indicate the position of a functional group or substituent within a molecule.
Numeric locants
The International Union of Pure and Applied Chemistry (IUPAC) recommends the use of n ...
number represents the location of a covalent bond
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 ...
in an organic compound
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The ...
, the position of which is variant between isomer
In chemistry, isomers are molecules or polyatomic ions with identical molecular formulae – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism is existence or possibility of isomers.
Iso ...
ic forms
* A simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
, simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set ...
, or convex hull
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ...
* In chemistry, the addition of heat in a reaction
* In legal shorthand
This is a list of abbreviations used in law and legal documents. It is common practice in legal documents to cite other publications by using standard abbreviations for the title of each source. Abbreviations may also be found for common words o ...
, it represents a defendant
In court proceedings, a defendant is a person or object who is the party either accused of committing a crime in criminal prosecution or against whom some type of civil relief is being sought in a civil case.
Terminology varies from one jurisdic ...
* In the financial markets, one of the Greeks
The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group and nation indigenous to the Eastern Mediterranean and the Black Sea regions, namely Greece, Cyprus, Albania, Italy, Turkey, Egypt, and, to a lesser extent, oth ...
, describing the rate of change of an option price for a given change in the underlying benchmark
* A major seventh chord
In music, a major seventh chord is a seventh chord in which the third is a major third above the root and the seventh is a major seventh above the root. The major seventh chord, sometimes also called a ''Delta chord'', can be written as maj7, M7, , ...
in jazz music notation
* In genetics
Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinian friar wor ...
, it can stand for a gene deletion
In genetics, a deletion (also called gene deletion, deficiency, or deletion mutation) (sign: Δ) is a mutation (a genetic aberration) in which a part of a chromosome or a sequence of DNA is left out during DNA replication. Any number of nucleoti ...
(e.g. the CCR5-Δ32
C-C chemokine receptor type 5, also known as CCR5 or CD195, is a protein on the surface of white blood cells that is involved in the immune system as it acts as a receptor for chemokines.
In humans, the ''CCR5'' gene that encodes the CCR5 pr ...
, a 32 nucleotide/bp deletion within CCR5)
* The American Dental Association
The American Dental Association (ADA) is an American professional association established in 1859 which has more than 161,000 members. Based in the American Dental Association Building in the Near North Side of Chicago, the ADA is the world's ...
cites it (together with omicron for "odont") as the symbol of dentistry.
* The anonymous signature of James David Forbes
James David Forbes (1809–1868) was a Scottish physicist and glaciologist who worked extensively on the conduction of heat and seismology. Forbes was a resident of Edinburgh for most of his life, educated at its University and a professor ...
.
* Determinacy (having a definite truth-value) in philosophical logic
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical ...
.
* In mathematics, the symbol ≜ (delta over equals) is occasionally used to define a new variable or function.
Lowercase
The lowercase letter δ (or 𝛿) can be used to denote:
* A change in the value of a variable in calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
* A functional derivative
In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a functional in this sense is a function that acts on functions) to a change in a function on ...
in functional calculus
In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately, several related areas) of the field of functional analysis, connected with spectral the ...
* An auxiliary function in calculus, used to rigorously define the limit
Limit or Limits may refer to:
Arts and media
* ''Limit'' (manga), a manga by Keiko Suenobu
* ''Limit'' (film), a South Korean film
* Limit (music), a way to characterize harmony
* "Limit" (song), a 2016 single by Luna Sea
* "Limits", a 2019 ...
or continuity of a given function
* The Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise:
\delta_ = \begin
0 &\text i \neq j, \\
1 &\ ...
in mathematics
* The degree of a vertex (graph theory)
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of ve ...
* The Dirac delta function
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire ...
in mathematics
* The transition function in automata
An automaton (; plural: automata or automatons) is a relatively self-operating machine, or control mechanism designed to automatically follow a sequence of operations, or respond to predetermined instructions.Automaton – Definition and More ...
* Deflection
Deflection or deflexion may refer to:
Board games
* Deflection (chess), a tactic that forces an opposing chess piece to leave a square
* Khet (game), formerly ''Deflexion'', an Egyptian-themed chess-like game using lasers
Mechanics
* Deflection ...
in engineering mechanics
* The force of interest in actuarial science
* The chemical shift
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of ...
of nuclear magnetic resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
in chemistry
* The relative electronegativity
Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the d ...
of different atoms in a molecule, δ− being more electronegative than δ+
* Text requiring deletion in proofreading
Proofreading is the reading of a galley proof or an electronic copy of a publication to find and correct reproduction errors of text or art. Proofreading is the final step in the editorial cycle before publication.
Professional
Traditional ...
; the usage is said to date back to classical times
* In some of the manuscripts written by Dr. John Dee
John Dee (13 July 1527 – 1608 or 1609) was an English mathematician, astronomer, astrologer, teacher, occultist, and alchemist. He was the court astronomer for, and advisor to, Elizabeth I, and spent much of his time on alchemy, divinatio ...
, the character of delta is used to represent Dee
* A subunit of the F1 sector of the F-ATPase
F-ATPase, also known as F-Type ATPase, is an ATPase/ synthase found in bacterial plasma membranes, in mitochondrial inner membranes (in oxidative phosphorylation, where it is known as Complex V), and in chloroplast thylakoid membranes. It use ...
* The declination
In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the ...
of an object in the equatorial coordinate system
The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fund ...
of 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 ...
* The dividend yield in the Black–Scholes option pricing formula
* Ratios of environmental isotopes The environmental isotopes are a subset of isotopes, both stable and radioactive, which are the object of isotope geochemistry. They are primarily used as tracers to see how things move around within the ocean-atmosphere system, within terrestrial b ...
, such as 18O/16O and D/1H from water are displayed using delta notation – δ18O and δD, respectively
* The rate of depreciation of the aggregate capital stock of an economy in an exogenous growth model
In a variety of contexts, exogeny or exogeneity () is the fact of an action or object originating externally. It contrasts with endogeneity or endogeny, the fact of being influenced within a system.
Economics
In an economic model, an exogeno ...
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 ...
* In a system that exhibits electrical reactance
In electrical circuits, reactance is the opposition presented to alternating current by inductance or capacitance. Greater reactance gives smaller current for the same applied voltage. Reactance is similar to resistance in this respect, but doe ...
, the angle between voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
and current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
* Partial charge A partial charge is a non-integer charge value when measured in elementary charge units. Partial charge is more commonly called net atomic charge. It is represented by the Greek lowercase letter 𝛿, namely 𝛿− or 𝛿+.
Partial charges are c ...
in chemistry
* The maximum birrefringence of a crystal in optical mineralogy
Optical mineralogy is the study of minerals and rocks by measuring their optical properties. Most commonly, rock and mineral samples are prepared as thin sections or grain mounts for study in the laboratory with a petrographic microscope. Optic ...
.
* An Old Irish
Old Irish, also called Old Gaelic ( sga, Goídelc, Ogham script: ᚌᚑᚔᚇᚓᚂᚉ; ga, Sean-Ghaeilge; gd, Seann-Ghàidhlig; gv, Shenn Yernish or ), is the oldest form of the Goidelic/Gaelic language for which there are extensive writt ...
voiced dental or alveolar fricative
A fricative is a consonant produced by forcing air through a narrow channel made by placing two articulators close together. These may be the lower lip against the upper teeth, in the case of ; the back of the tongue against the soft palate in t ...
of uncertain articulation, the ancestor of the sound represented by Modern Irish
Irish (Standard Irish: ), also known as Gaelic, is a Goidelic language of the Insular Celtic branch of the Celtic language family, which is a part of the Indo-European language family. Irish is indigenous to the island of Ireland and was the ...
''dh''
Computer encodings
* Greek Delta / Coptic Dalda
* Latin Delta
Latin delta (ẟ, lower-case only) is a Latin letter similar in appearance to the Greek lowercase letter delta (δ), but derived from the handwritten Latin lowercase d. It is also known as "script d" or "insular d" and is used in medieval Welsh t ...
* Technical and Mathematical symbols
* Mathematical Delta
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
{{Wiktionary, Δ, δ
* ∆ (disambiguation)
* D, d
* Д, д
* ẟ - Latin delta
* ∂
The character ∂ (Unicode: U+2202) is a stylized cursive '' d'' mainly used as a mathematical symbol, usually to denote a partial derivative such as / (read as "the partial derivative of ''z'' with respect to ''x''"). It is also used for the bo ...
- the partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Part ...
symbol, sometimes mistaken for a lowercase Greek letter Delta.
* ð - the small eth
(colloquially)
, former_name = eidgenössische polytechnische Schule
, image = ETHZ.JPG
, image_size =
, established =
, type = Public
, budget = CHF 1.896 billion (2021)
, rector = Günther Dissertori
, president = Joël Mesot
, a ...
appears similar to a small delta, and also represents a ''d'' sound in some contexts
* Th (digraph)
Th is a digraph in the Latin script. It was originally introduced into Latin to transliterate Greek loan words. In modern languages that use the Latin alphabet, it represents a number of different sounds. It is the most common digraph in order of ...
* Thorn (letter)
Thorn or þorn (Þ, þ) is a letter in the Old English, Old Norse, Old Swedish, and modern Icelandic alphabets, as well as modern transliterations of the Gothic alphabet, Middle Scots, and some dialects of Middle English. It was also used in me ...
* 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 ...
* ∇ - Nabla symbol
The nabla symbol
The nabla is a triangular symbol resembling an inverted Greek delta:Indeed, it is called ( ανάδελτα) in Modern Greek. \nabla or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word f ...
* Delta Air Lines
Delta Air Lines, Inc., typically referred to as Delta, is one of the major airlines of the United States and a legacy carrier. One of the List of airlines by foundation date, world's oldest airlines in operation, Delta is headquartered in Atla ...
* SARS-CoV-2 Delta variant
The Delta variant (B.1.617.2) was a variant of SARS-CoV-2, the virus that causes COVID-19. It was first detected in India in late 2020. The Delta variant was named on 31 May 2021 and had spread to over 179 countries by 22 November 2021. The ...
References
Greek letters