Delta (letter)

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: (6) · (90) · (900)
In other languages
Bactrian  · Coptic  · Albanian
Scientific symbols
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Delta (uppercase Δ, lowercase δ; δέλτα; Modern Greek [ˈðelta] dhélta) 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).

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

Pronunciation

In Ancient Greek, 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.

Mathematics and the Sciences

Upper case

The upper-case letter Δ can be used to denote

• Change of any variable quantity, in mathematics and the sciences; for example, in

${y_2-y_1\over x_2-x_1} = {\Delta y \over \Delta x}$, the average change of y per unit x, i.e. the change of y over the change of x

• More specifically, the difference operator.^[1]
• 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:

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

• A macroscopic change in the value of a variable in mathematics or science
• Uncertainty in a physical variable as seen in for instance the uncertainty principle
• An interval of possible values for a given quantity for instance across a sample^{[citation needed]}
• 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
• In chemistry, it is often used to represent the addition of heat in a reaction.
• In legal shorthand, it represents a defendant
• In the financial markets, it is one of the Greeks 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 Daedalus
• 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.^[2]

Lower case

The lower-case letter δ can be used to denote

• An infinitesimal change in the value of a variable in infinitesimal 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
• 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
• The Computer Science chapter at the Royal Institute of Technology^[3]
• Is 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 on the Black-Scholes option pricing formula
• Signifies a major seventh chord in jazz music notation.
• Ratios of environmental isotopes, such as ¹⁸O/¹⁶O and D/¹H from waters 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.^[4]

Meteorology

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

See also

• D, d
• Д, д
• Th (digraph)
• Greek letters used in mathematics, science, and engineering
• Nabla symbol ($\nabla$)
• ∂ - the partial derivative symbol, sometimes mistaken for a lowercase Greek letter Delta.
• ẟ - Latin delta

References

1. ^ http://ocw.mit.edu/high-school/courses/highlights-of-calculus/big-picture-of-calculus/
2. ^ ADA.org: Oral Health Topics: Emblem/Insignia of Dentistry^{[dead link]}
3. ^ "Konglig Datasektionen, Statutes, §2.2 Symbol". D.kth.se. http://www.d.kth.se/sektionen/formalia/stadgar/#paragraf2.2. Retrieved 2010-09-07. 
4. ^ [1]^{[dead link]}