Delta (letter)

Template:Short description Template:RedirectTemplate:Distinguish Template:Refimprove Template:Greek AlphabetDelta (Template:IPAc-en Template:Respell; uppercase Δ, lowercase δ; Template:Langx, délta, Template:IPA) 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,Template:Vague this use of the word delta was not coined by Herodotus.

Pronunciation

In Ancient Greek, delta represented a voiced dental plosive Template:IPA. In Modern Greek, it represents a voiced dental fricative Template:IPA, like the "th" in "that" or "this" (while Template: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 $\frac{y_2-y_1}{x_2-x_1}=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}$, 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 Template:Lang, 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:

  $\mathrm{\Delta }f=\sum _{i=1}^n\frac{{\partial }^{2}f}{\partial x_i^2}$.

• The discriminant of a polynomial equation, especially the quadratic equation:

  $\mathrm{\Delta }=b^2-4ac$.

• The area of a triangle:

  $\mathrm{\Delta }=\frac{1}{2}ab\sin C$.

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

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

• Template:Unichar
• Template:Unichar (Template:Tt in TeX)
• Template:Unichar (Template:Tt in TeX)
• Template:Unichar
• Template:Unichar
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• Template:Unichar
• Template:Unichar
• Template:UnicharTemplate:Efn
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See also

• 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