Delta (letter)
Encyclopedia
Delta is the fourth letter of the Greek alphabet
. In the system of Greek numerals
it has a value of 4. It was derived from the Phoenician letter
Dalet. Letters that come from delta include Latin
D
and Cyrillic
Д
.
A river delta
(originally, the Nile River delta) is so named because its shape approximates the uppercase letter delta (the shape is a triangle).
, it represented a voiced dental plosive
/d/. In Modern Greek
, it represents a voiced dental fricative
/ð/, like the "th" in "that" or "this". It is romanized as d or dh.
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...
. In the system of Greek numerals
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...
it has a value of 4. It was derived from the Phoenician letter
Phoenician alphabet
The Phoenician alphabet, called by convention the ProtoCanaanite alphabet for inscriptions older than around 1050 BC, was a nonpictographic consonantal alphabet, or abjad. It was used for the writing of Phoenician, a Northern Semitic language, used by the civilization of Phoenicia...
Dalet. Letters that come from delta include Latin
Latin alphabet
The Latin alphabet, also called the Roman alphabet, is the most recognized alphabet used in the world today. It evolved from a western variety of the Greek alphabet called the Cumaean alphabet, which was adopted and modified by the Etruscans who ruled early Rome...
D
D
D is the fourth letter in the basic modern Latin alphabet. History :The Semitic letter Dâlet may have developed from the logogram for a fish or a door. There are various Egyptian hieroglyphs that might have inspired this. In Semitic, Ancient Greek, and Latin, the letter represented ; in the...
and Cyrillic
Cyrillic alphabet
The Cyrillic script or azbuka is an alphabetic writing system developed in the First Bulgarian Empire during the 10th century AD at the Preslav Literary School...
Д
De (Cyrillic)
De is a letter of the Cyrillic alphabet.De commonly represents the voiced dental plosive , like the pronunciation of ⟨d⟩ in admit.De is romanized using the Latin letter D.History:...
.
A river delta
River delta
A delta is a landform that is formed at the mouth of a river where that river flows into an ocean, sea, estuary, lake, reservoir, flat arid area, or another river. Deltas are formed from the deposition of the sediment carried by the river as the flow leaves the mouth of the river...
(originally, the Nile River delta) is so named because its shape approximates the uppercase letter delta (the shape is a triangle).
Pronunciation
In Ancient GreekAncient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
, it represented a voiced dental plosive
Voiced dental plosive
The voiced dental plosive is a type of consonantal sound, used in some spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is...
/d/. In Modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...
, it represents a voiced dental fricative
Voiced dental fricative
The voiced dental nonsibilant fricative is a type of consonantal sound, used in some spoken languages. The symbol in the International Phonetic Alphabet that represents this sound, eth, is . The symbol was taken from the Old English letter eth, which could stand for either a voiced or unvoiced...
/ð/, like the "th" in "that" or "this". It is romanized as d or dh.
Upper case
The uppercase letter Δ can be used to denote Change of any variable quantity, in mathematics and the sciences; for example, in

 , the average change of y per unit x, i.e. the change of y over the change of x
 More specifically, the difference operator.
 The Laplace operatorLaplace operatorIn mathematics the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇2 or Δ...
:  The discriminantDiscriminantIn algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial's roots. For example, the discriminant of the quadratic polynomialax^2+bx+c\,is\Delta = \,b^24ac....
of a polynomialPolynomialIn mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and nonnegative integer exponents...
equation, especially the quadratic equationQuadratic equationIn mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
:  A macroscopic changeDerivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
in the value of a variable in mathematics or science  UncertaintyUncertaintyUncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
in a physical variable as seen in for instance the uncertainty principleUncertainty principleIn quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...  An interval of possible values for a given quantity for instance across a sample
 Any of the delta particlesDelta baryonThe Delta baryons are a family of subatomic hadron particles which have the symbols , , , and and electric charges +2, +1, 0 and 1 elementary charge respectively...
in particle physics  The determinant of the matrix of coefficients of a set of linear equations (see Cramer's RuleCramer's ruleIn linear algebra, Cramer's rule is a theorem, which gives an expression for the solution of a system of linear equations with as many equations as unknowns, valid in those cases where there is a unique solution...
)  That an associated locantLocantIn organic chemistry, a locant is a figure to indicate the position of a functional group within a molecule . Example :There are at least two isomers of the linear form of pentanone, a ketone that contains a chain of exactly five carbon atoms...
number represents the location of a covalent bondCovalent bondA covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
in an organic compoundOrganic compoundAn organic compound is any member of a large class of gaseous, liquid, or solid chemical compounds whose molecules contain carbon. For historical reasons discussed below, a few types of carboncontaining compounds such as carbides, carbonates, simple oxides of carbon, and cyanides, as well as the...
, the position of which is variant between isomeric forms  In chemistry, it is often used to represent the addition of heat in a reaction.
 In legal shorthand, it represents a defendantDefendantA defendant or defender is any party who is required to answer the complaint of a plaintiff or pursuer in a civil lawsuit before a court, or any party who has been formally charged or accused of violating a criminal statute...
 In the financial markets, it is one of the GreeksGreeks (finance)In mathematical finance, the Greeks are the quantities representing the sensitivities of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of...
that describes the rate of change of an option price for a given change in the underlying benchmark  It is the symbol of the Greek inventor and architect DaedalusDaedalusIn Greek mythology, Daedalus was a skillful craftsman and artisan.Family:...
 In geneticsGeneticsGenetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....
, it can stand for a gene deletion, e.g. the CCR5Δ32 a deletion of the CCR5 at the 32nd base pair segment  The American Dental Association cites it (together with omicron for "odont") as the symbol of dentistry.
 , the average change of y per unit x, i.e. the change of y over the change of x
Lower case
The lowercase letter δ can be used to denote An infinitesimal change in the value of a variable in infinitesimal calculusInfinitesimal calculusInfinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
 An auxiliary function in CalculusCalculusCalculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
used to rigorously define the limitLimit of a functionIn mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input....
or continuityContinuous functionIn mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
of a given function.  The Kronecker delta in mathematics
 The Dirac delta functionDirac delta functionThe Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...
in mathematics  The transition function in automataFinite state machineA finitestate machine or finitestate automaton , or simply a state machine, is a mathematical model used to design computer programs and digital logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states...
 DeflectionDeflection (engineering)In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.The deflection distance of a member under a load is directly related to the slope of the deflected shape of the member under that load and can be calculated by...
in engineering mechanics  The Force of InterestCompound interestCompound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
in actuarial science  The chemical shiftChemical shiftIn nuclear magnetic resonance spectroscopy, the chemical shift is the resonant frequency of a nucleus relative to a standard. Often the position and number of chemical shifts are diagnostic of the structure of a molecule...
of Nuclear Magnetic ResonanceNuclear magnetic resonanceNuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and reemit electromagnetic radiation...
in chemistry  The relative electronegativityElectronegativityElectronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...
of different atoms in a molecule, δ^{−} being more electronegative than δ^{+}  Text requiring deletion in proofreadingProofreadingProofreading is the reading of a galley proof or computer monitor to detect and correct productionerrors of text or art. Proofreaders are expected to be consistently accurate by default because they occupy the last stage of typographic production before publication.Traditional method:A proof is...
. The usage is said to date back to classical times  In some of the manuscripts written by Dr. John DeeJohn Dee (mathematician)John Dee was an English mathematician, astronomer, astrologer, occultist, navigator, imperialist and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy....
, the character of delta is used to represent Dee  The Computer Science chapter at the Royal Institute of TechnologyRoyal Institute of TechnologyThe Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for onethird of Sweden’s technical research and engineering education...
 Is a subunit of the F1 sector of the FATPaseFATPaseFATPase, also known as FType ATPase , is an ATPase found in bacterial plasma membranes, in mitochondrial inner membranes, and in chloroplast thylakoid membranes...
 The declinationDeclinationIn astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
of an object in the equatorial coordinate systemEquatorial coordinate systemThe equatorial coordinate system is a widelyused method of mapping celestial objects. It functions by projecting the Earth's geographic poles and equator onto the celestial sphere. The projection of the Earth's equator onto the celestial sphere is called the celestial equator...
of astronomyAstronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...  The dividend yield on the Black–Scholes option pricing formula
 Signifies a major seventh chord in jazz music notation.
 Ratios of environmental isotopesEnvironmental isotopesThe environmental isotopes are a subset of the isotopes, both stable and radioactive, which are the object of Isotope geochemistry.The most used environmental isotopes are:* deuterium* tritium* carbon13* carbon14* nitrogen15* oxygen18...
, such as ^{18}O/^{16}O and DDeuteriumDeuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...
/^{1}H from waters are displayed using delta notationIsotope geochemistryIsotope geochemistry is an aspect of geology based upon study of the relative and absolute concentrations of the elements and their isotopes in the Earth. Variations in the abundance of these isotopes, typically measured with an isotope ratio mass spectrometer or an accelerator mass spectrometer,...
 δ^{18}O and δD, respectively  The rate of depreciation of the aggregate capital stock of an economy in an exogenous growth modelExogenous growth modelThe neoclassical growth model, also known as the Solow–Swan growth model or exogenous growth model, is a class of economic models of longrun economic growth set within the framework of neoclassical economics...
in macroeconomicsMacroeconomicsMacroeconomics is a branch of economics dealing with the performance, structure, behavior, and decisionmaking of the whole economy. This includes a national, regional, or global economy...
.
Meteorology
 The name Delta was used as a name during the 1972 Atlantic hurricane season1972 Atlantic hurricane seasonThe 1972 Atlantic hurricane season officially began on June 1, 1972, and lasted until November 30, 1972. These dates conventionally delimit the period of each year when most tropical cyclones form in the Atlantic basin. A strong El Niño kept hurricane activity at a minimum, and in fact the season...
and the 2005 Atlantic hurricane season2005 Atlantic hurricane seasonThe 2005 Atlantic hurricane season was the most active Atlantic hurricane season in recorded history, repeatedly shattering numerous records. The impact of the season was widespread and ruinous with an estimated 3,913 deaths and record damage of about $159.2 billion...
as Tropical Storm Delta (2005)Tropical Storm Delta (2005)TropicalStorm Delta was a lateforming tropical storm of the 2005 Atlantic hurricane season which struck the Canary Islands as a strong extratropical storm, causing significant damage and then crossed over Morocco before dissipating...
.
See also
 D, dDD is the fourth letter in the basic modern Latin alphabet. History :The Semitic letter Dâlet may have developed from the logogram for a fish or a door. There are various Egyptian hieroglyphs that might have inspired this. In Semitic, Ancient Greek, and Latin, the letter represented ; in the...
 Д, дDe (Cyrillic)De is a letter of the Cyrillic alphabet.De commonly represents the voiced dental plosive , like the pronunciation of ⟨d⟩ in admit.De is romanized using the Latin letter D.History:...
 ẟ  Latin delta
 ∂  the partial derivativePartial derivativeIn 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...
symbol, sometimes mistaken for a lowercase Greek letter Delta.  Th (digraph)Th (digraph)Th is a digraph in the Roman alphabet. It is the most common digraph in order of frequency in the English language.Cluster /t.h/:The most literal use of ⟨th⟩ is to represent a consonant cluster of /t/ and /h/ as in English knighthood...
 Greek letters used in mathematics, science, and engineering
 Nabla symbolNabla symbolrightthumb256pxThe [[harp]], the instrument after which the nabla symbol is namedNabla is the symbol \nabla . The name comes from the Greek word for a Hebrew harp, which had a similar shape. Related words also exist in Aramaic and Hebrew. The symbol was first used by William Rowan Hamilton in...
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