Delta (letter)

Delta (uppercase Δ, lowercase δ; Δέλτα Délta; Modern Greek [ˈðelta]) 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).

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.

The upper-case letter Δ can be used to denote

Change of any variable quantity, in mathematics and the sciences (More specifically, the difference operator.^[1]); 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

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

\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]

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]