Delta (letter)

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Delta (uppercase ?, lowercase ? or ?; Greek: ????? délta, ['ðelta]) 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 ?.

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). Despite a popular legend, this use of the word delta was not coined by Herodotus.

Video Delta (letter)

Pronunciation

In Ancient Greek, delta 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.

Maps Delta (letter)

Upper case

The upper-case letter ? can be used to denote:

• Change of any changeable quantity, in mathematics and the sciences (more specifically, the difference operator); for example, in:

${\displaystyle {y_{2}-y_{1} \over x_{2}-x_{1}}={\Delta y \over \Delta x},}$

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 ??????? 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.)

• 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, describing 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-?32, 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.

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Lower case

The lower-case letter ? (or ?) can be used to denote:

• A change in the value of a variable in calculus
• An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function
• The Kronecker delta in mathematics
• The degree of a vertex (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, ?^- being more electronegative than ?⁺
• 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 - ?¹⁸O and ?D , 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

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Computer encodings

• Greek Delta / Coptic Dalda

• Latin Delta

• Technical and Mathematical symbols

• Mathematical Delta

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

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See also

• ? (disambiguation)
• D, d
• ?, ?
• ? - Latin delta
• ? - the partial derivative symbol, 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)
• Greek letters used in mathematics, science, and engineering
• ? - Nabla symbol

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References

Source of article : Wikipedia