Delta (letter)

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Greek alphabet
Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
History
Archaic local variants
Ligatures (ϛ, ȣ, ϗ) Diacritics
Numerals ϛ (6) ϟ (90) ϡ (900)
In other languages
Bactrian Coptic Albanian
Scientific symbols
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Delta (uppercase Δ, lowercase δ or 𝛿; Δέλτα{{#invoke:Category handler|main}} Délta; Modern Greek Template:IPA-el) 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 upper-case letter delta (the shape is a triangle). Despite a popular legend, this use of the word delta was not coined by Herodotus.

Pronunciation

In Ancient Greek, delta 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.

Upper case

The upper-case letter Δ can be used to denote:

• Change of any changeable quantity, in mathematics and the sciences (more specifically, the difference operator{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B=

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${y_{2}-y_{1} \over x_{2}-x_{1}}={\Delta y \over \Delta x},$

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 letter d is used in much the same way for the notation of derivatives and differentials, which also describe change.)

• The Laplace operator:

$\Delta f=\sum _{i=1}^{n}{\frac {\partial ^{2}f}{\partial x_{i}^{2}}}$

• The discriminant of a polynomial equation, especially the quadratic equation:

$\Delta =b^{2}-4ac\,\!$

• The symmetric difference of two sets
• A macroscopic change in the value of a variable in mathematics or science
• Uncertainty in a physical variable as seen in the uncertainty principle
• An interval of possible values for a given quantity (i.e. across a sample{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B=

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• 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)
• That an associated locant number represents the location of a covalent bond in an organic compound, the position of which is variant between isomeric forms
• A simplex, simplicial complex, or convex hull
• In chemistry, the addition of heat in a reaction
• In legal shorthand, it represents a defendant.
• In the financial markets, one of the Greeks, describing the rate of change of an option price for a given change in the underlying benchmark
• The symbol of the Greek inventor and architect Daedalus
• A major seventh chord in jazz music notation
• In genetics, it can stand for a gene deletion (e.g. the CCR5-Δ32, 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.
• English indie rock band Alt-J (so known because the symbol can be typed on a Mac OS X computer system by pressing Alt-J)

Lower case

The alphabet on a black figure vessel, with a D-shaped delta.

The lower-case letter δ (or 𝛿) can be used to denote:

• A change in the value of a variable in calculus
• An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function
• The Kronecker delta in mathematics
• The Dirac delta function in mathematics
• In mathematics (specifically point-set topology), the boundary of a set A is denoted by δA .
• The transition function in automata
• 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
• 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 and current

Meteorology

• Delta was used as a name during the 1972 Atlantic hurricane season and the 2005 Atlantic hurricane season as Tropical Storm Delta (2005).

Keyboard Entry

On Microsoft Windows, a small delta can be generated by typing Template:Key pressTemplate:Key pressTemplate:Key press.

In certain programs (e.g. Microsoft Word), an uppercase delta can be typed using Template:Key pressTemplate:Key pressTemplate:Key pressTemplate:Key press. However, in most other programs, Template:Key pressTemplate:Key pressTemplate:Key pressTemplate:Key press generates a closing quotation mark (”).

Computer encodings

• Greek Delta / Coptic Dalda

• Latin Delta

• 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

• D, d
• Д, д
• ẟ - 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)
• Greek letters used in mathematics, science, and engineering
• ∇ - Nabla symbol