Delta (letter)

Delta (letter)

Delta ( DEL-tə; uppercase Δ, lowercase δ; Greek: δέλτα, délta, [ˈðelta]) 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

Delta (letter)

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

Uppercase

Delta (letter)

• Change of any changeable quantity, in mathematics and the sciences (in particular, the difference operator); for example, in ${\displaystyle {\frac {y{2}-y{1}}{x{2}-x{1}}}={\frac {\Delta y}{\Delta x}}}$, 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: ${\displaystyle \Delta f=\sum {i=1}^{n}{\frac {\partial ^{2}f}{\partial x{i}^{2}}}}$. • The discriminant of a polynomial equation, especially the quadratic equation: ${\displaystyle \Delta =b^{2}-4ac}$. • The area of a triangle: ${\displaystyle \Delta ={\tfrac {1}{2}}ab\sin {C}}$. • 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

Delta (letter)

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

Delta (letter)

• U+018D ƍ LATIN SMALL LETTER TURNED DELTA • U+0394 Δ GREEK CAPITAL LETTER DELTA (Δ) (\Delta in TeX) • U+03B4 δ GREEK SMALL LETTER DELTA (δ) (\delta in TeX) • U+1D5F ᵟ MODIFIER LETTER SMALL DELTA • U+1E9F ẟ LATIN SMALL LETTER DELTA • U+2207 ∇ NABLA (∇, ∇) • U+225C ≜ DELTA EQUAL TO (≜, ≜) • 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