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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 ...
. 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 those ...
it has a value of 4. It was derived from the Phoenician letter dalet 𐤃. Letters that come from delta include
Latin Latin (, or , ) is a classical language belonging to the Italic languages, 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 ...
D and Cyrillic Д. A
river delta A river delta is a landform shaped like a triangle, created by 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, reservoir, or (more rare ...
(originally, the delta 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 riv ...
) 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 fo ...
.


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 pe ...
, 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 , like the "th" in "that" or "this" (while in foreign words is instead commonly transcribed as ντ). Delta is romanized 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 operatoronline copy
/ref>); for example, in:\frac = \frac ,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 languages, 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 ...
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. ...
s and differentials, which also describe change by infinitesimal amounts.) * The Laplace operator: *:\Delta f = \sum_^n * The discriminant 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 exampl ...
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 value, and , , and represent known numbers, where . (If and then the equation is linear, not qu ...
: *:\Delta = b^2 - 4ac * The area of a triangle *:\Delta = \tfrac a b \sin * The symmetric difference 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 ...
in a physical variable as seen in the uncertainty principle * 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 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 ato ...
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. Th ...
, the position of which is variant between isomeric 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, or convex hull * In chemistry, the addition of heat in a reaction * In legal shorthand, 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 jurisd ...
* 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, ot ...
, describing the rate of change of an option price for a given change in the underlying benchmark * A major seventh chord 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 work ...
, 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 nucleot ...
(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. * 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 mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
* 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 w ...
in functional calculus * 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 degree of a vertex (graph theory) * The Dirac delta function in mathematics * The transition function in automata *
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 of nuclear magnetic resonance in chemistry * The relative electronegativity of different atoms in a molecule, δ being more electronegative than δ+ * Text requiring deletion in proofreading; the usage is said to date back to classical times * In some of the manuscripts written by Dr. John Dee, the character of delta is used to represent Dee * A subunit of the F1 sector of the F-ATPase * The declination of an object in the equatorial coordinate system of
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
* The dividend yield in the Black–Scholes option pricing formula * Ratios of environmental isotopes, 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 macroeconomics * In a system that exhibits electrical reactance, 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 ...
and current * Partial charge in chemistry * The maximum birrefringence of a crystal in optical mineralogy. * 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 writte ...
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 ...
of uncertain articulation, the ancestor of the sound represented by Modern Irish ''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 ...
* 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 * - Latin delta * - the partial derivative symbol, sometimes mistaken for a lowercase Greek letter Delta. * ð - the small eth appears similar to a small delta, and also represents a ''d'' sound in some contexts * Th (digraph) * Thorn (letter) * Greek letters used in mathematics, science, and engineering * ∇ - Nabla symbol *
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 world's oldest airlines in operation, Delta is headquartered in Atlanta, Georgia. The airline, along ...
*
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