Delta

Delta (uppercase Δ, lowercase δ; δέλτα; Modern Greek Template:IPA-el dhélta) 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. Letters that come from delta include Latin D and Cyrillic Д.

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).

Greek

In Ancient Greek, it represented a voiced dental plosive /d/. In Modern Greek, it represents a voiced dental fricative /ð/, like the "th" in "that" or "this". It is romanized as d or dh.

Math and science

Upper case

The upper-case letter Δ can be used to denote

• Change any type; (in science and engineering fields)
• Change; e.g. in

<math>{y_2-y_1\over x_2-x_1} = {\Delta y \over \Delta x}</math>, the average change of y per unit x, i.e. the change of y over the change of x

• More specifically, the difference operator<ref>http://ocw.mit.edu/high-school/courses/highlights-of-calculus/big-picture-of-calculus/</ref>.
• The Laplace operator:

<math>\Delta f = \sum_{i=1}^n {\frac{\partial^2 f}{\partial x_i^2}}</math>

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

<math>\Delta = b^2 - 4ac\,\!</math>

• 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 sampleTemplate:Citation needed
• 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.<ref>ADA.org: Oral Health Topics: Emblem/Insignia of DentistryTemplate:Dead link</ref>

Lower case

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<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 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.<ref>[1]Template:Dead link</ref>

See also

• D, d
• Д, д
• Th
• Greek letters used in mathematics, science, and engineering
• Nabla symbol (<math>\nabla</math>)
• ∂ - the partial derivative symbol, sometimes mistaken for a lowercase Greek letter Delta.