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
Other characters
	Digamma		Stigma
	Heta		San
	Qoppa		Sampi
Greek diacritics

Delta (uppercase Δ, lowercase δ; Greek: Δέλτα [ˈðelta], Dhelta) 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. In the Ancient Greek language, it represented a voiced dental plosive /d/, while in Modern Greek it represents a voiced dental fricative /ð/, hence it is pronounced as "th" in "that" or "this". It is romanised as either "D" or "Dh."

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).

1 The upper-case letter Δ
2 The lower-case letter δ
3 See also
4 References

The upper-case letter Δ

The upper-case letter Δ can be used to denote

Change any type; (in science and engineering fields)
Change; e.g. 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.
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
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.^[1]

The lower-case letter δ

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^[2]
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.^[3]

References

↑ ADA.org: Oral Health Topics: Emblem/Insignia of Dentistry
↑ "Konglig Datasektionen, Statutes, §2.2 Symbol". D.kth.se. http://www.d.kth.se/sektionen/formalia/stadgar/#paragraf2.2. Retrieved 2010-09-07.
↑ [1]

Delta (letter)

Contents

The upper-case letter Δ

The lower-case letter δ

See also

References