# 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 :
| Ϝϝ | Digamma | Ͱͱ | Heta |
| Ϻϻ | San | Ϙϙ | Koppa |
| Ͷͷ | TsanDigamma | Ͳͳ | Sampi |
| Ϸϸ | Sho | | |
Diacritics and other symbols :
Diacritics
άὰᾶἀἁᾱᾰϊᾳσ̌
Ligatures
ȢȢϏϗϚϛ⳨☧
Numerals (Attic)
ϛ (6)ϟ (90)ϡ (900) :
Related topics :
Use as scientific symbols
Orthography
Romanization
Cyrillization :
Category :
vte :
Delta (/ˈdɛltə/ DEL-tə; uppercase Δ, lowercase δ; Greek: δέλτα, 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 IPA:. In Modern Greek, it represents a voiced dental fricative IPA:, like the "th" in "that" or "this" (while IPA: 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 operator); for example, in ${\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {\Delta y}{\Delta x}}$, 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 by infinitesimal amounts.)
* 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 area of a triangle:
    $\Delta ={\tfrac {1}{2}}ab\sin {C}$.
* 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 $^{18}$O/$^{16}$O and D/$^1$H from water are displayed using delta notation – δ$^{18}$O 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

* U+018D ƍ LATIN SMALL LETTER TURNED DELTA
* U+0394 Δ GREEK CAPITAL LETTER DELTA (&Delta;) (\Delta in TeX)
* U+03B4 δ GREEK SMALL LETTER DELTA (&delta;) (\delta in TeX)
* U+1D5F ᵟ MODIFIER LETTER SMALL DELTA
* U+1E9F ẟ LATIN SMALL LETTER DELTA
* U+2207 ∇ NABLA (&Del;, &nabla;)
* U+225C ≜ DELTA EQUAL TO (&triangleq;, &trie;)
* U+234B ⍋ APL FUNCTIONAL SYMBOL DELTA STILE
* U+234D ⍍ APL FUNCTIONAL SYMBOL QUAD DELTA
* U+2359 ⍙ APL FUNCTIONAL SYMBOL DELTA UNDERBAR
* U+2C86 Ⲇ COPTIC CAPITAL LETTER DALDA
* U+2C87 ⲇ COPTIC SMALL LETTER DALDA
* U+1D6AB 𝚫 MATHEMATICAL BOLD CAPITAL DELTA
* U+1D6C5 𝛅 MATHEMATICAL BOLD SMALL DELTA
* U+1D6E5 𝛥 MATHEMATICAL ITALIC CAPITAL DELTA
* U+1D6FF 𝛿 MATHEMATICAL ITALIC SMALL DELTA
* U+1D71F 𝜟 MATHEMATICAL BOLD ITALIC CAPITAL DELTA
* U+1D739 𝜹 MATHEMATICAL BOLD ITALIC SMALL DELTA
* U+1D759 𝝙 MATHEMATICAL SANS-SERIF BOLD CAPITAL DELTA
* U+1D773 𝝳 MATHEMATICAL SANS-SERIF BOLD SMALL DELTA
* U+1D793 𝞓 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL DELTA
* U+1D7AD 𝞭 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL DELTA
* ↑ The MATHEMATICAL codes should only be used in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.