𝛿

Delta ( ; uppercase Δ, lowercase δ; , ''délta'', ) is the fourth letter of the Greek alphabet. In the system of Greek numerals, it has a value of four. It was derived from the Phoenician letter dalet 𐤃. Letters that come from delta include the Latin D and the Cyrillic Д.

A river delta (originally, the delta of the Nile River) is named so because its shape approximates the triangular uppercase letter delta. Contrary to a popular legend, this use of the word ''delta'' was not coined by Herodotus.

Pronunciation

In Ancient Greek, delta represented a voiced dental plosive . In Modern Greek, it represents a voiced dental fricative , like the "''th''" in "''that''" or "''this''" (while in foreign words is instead commonly transcribed as ντ). Delta is romanized as ''d'' or ''dh''.

Uppercase

The uppercase letter Δ is used to denote:
* Change of any changeable quantity, in mathematics and the sciences (in particular, the difference operatoronline copy
/ref>); for example, in $\frac=\frac$, 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 , ''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 by infinitesimal amounts.)
* The Laplace operator:
*: $\Delta f=\sum_^n$.
* The discriminant of a polynomial equation, especially the quadratic equation:
*: $\Delta=b^2-4ac$.
* The area of a triangle:
*: $\Delta=\tfracab\sin$.
* 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.
* 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, describes the rate of change of an option price for a given change in the underlying benchmark.
* A major seventh chord in jazz music notation.
* In genetics, it can stand for a gene deletion (e.g. the CCR5-Δ32, a 32 nucleotide/bp deletion within CCR5).
* The American Dental Association cites it (together with omicron for "odont") as the symbol of dentistry.
* The anonymous signature of James David Forbes.
* Determinacy (having a definite truth-value) in philosophical logic.
* In mathematics, the symbol ≜ (delta over equals) is occasionally used to define a new variable or function.

Lowercase

The lowercase letter δ (or 𝛿) can be used to denote:
* A change in the value of a variable in calculus.
* A functional derivative in functional calculus.
* The (ε, δ)-definition of limits, in mathematics and more specifically in calculus.
* The Kronecker delta in mathematics.
* The central difference for a function.
* The degree of a vertex in graph theory.
* 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.
* 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.
* Partial charge in chemistry.
* The maximum birefringence of a crystal in optical mineralogy.
* An Old Irish voiced dental or alveolar fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish ''dh''.
* Silver ratio

Unicode

*
* ( in TeX)
* ( in TeX)
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*

See also

{{Wiktionary, Δ, δ
* Arrow (symbol)
* Chevron (insignia)
* ∆ (disambiguation)
* D, d
* Д, д
* ẟ – Latin delta
* ∂ – the partial derivative symbol, a curved ''d'', 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)
* Thorn (letter)
* Greek letters used in mathematics, science, and engineering
* ∇ – Nabla symbol
* Delta Air Lines
* SARS-CoV-2 Delta variant

References

Greek letters