Delta

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Δ δ Delta
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'''Delta''' (uppercase '''Δ''', lowercase '''δ'''; {{lang|el|δέλτα}}; Modern Greek {{IPA-el|ˈðelta|}} ''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 alphabet|Phoenician letter]] [[Dalet (letter)|Dalet]]. Letters that come from delta include [[Latin alphabet|Latin]] [[D]] and [[Cyrillic alphabet|Cyrillic]] [[De (Cyrillic)|Д]].
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Delta (uppercase Δ, lowercase δ; Greek: Δέλτα [ðelta] Thelta) 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, but in the Ancient Greek language..
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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).
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A river delta is so named because its shape approximates the upper-case letter delta.
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==Greek==
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In [[Ancient Greek]], it represented a [[voiced dental plosive]] {{IPA|/d/}}. In [[Modern Greek]], it represents a [[voiced dental fricative]] {{IPA|/ð/}}, like the "th" in "that" or "this". It is [[romanization of Greek|romanized]] as ''d'' or ''dh''.
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==Math and science==
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===Upper case===
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The upper-case letter Δ can be used to denote
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*[[Change (mathematics)|Change]] any type; (in science and engineering fields)
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*[[Difference operator|Change]]; e.g. in
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::<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
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*More specifically, the [[difference operator]]<ref>http://ocw.mit.edu/high-school/courses/highlights-of-calculus/big-picture-of-calculus/</ref>.
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*The [[Laplace operator]]:
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:<math>\Delta f = \sum_{i=1}^n {\frac{\partial^2 f}{\partial x_i^2}}</math>
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*The [[discriminant]] of a [[polynomial]] equation, especially the [[quadratic equation]]:
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:<math>\Delta = b^2 - 4ac\,\!</math>
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*A [[derivative|macroscopic change]] in the value of a variable in mathematics or science
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*[[Uncertainty]] in a physical variable as seen in for instance the [[uncertainty principle]]
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*An interval of possible values for a given quantity for instance across a sample{{Citation needed|date=August 2008}}
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*Any of the [[Delta baryon|delta particles]] in particle physics
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*The determinant of the matrix of coefficients of a set of linear equations (see [[Cramer's Rule]])
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*That an associated [[locant]] number represents the location of a [[covalent bond]] in an [[organic compound]], the position of which is variant between [[isomers|isomeric]] forms
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*In chemistry, it is often used to represent the addition of heat in a reaction.
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*In [[legal shorthand]], it represents a [[defendant]]
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*In the financial markets, it is one of the [[Greeks (finance)|Greeks]] that describes the rate of change of an option price for a given change in the underlying benchmark
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* It is the symbol of the Greek inventor and architect [[Daedalus]]
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*In [[genetics]], it can stand for a [[Deletion (genetics)|gene deletion]], e.g. the [[CCR5-Δ32]] a deletion of the CCR5 at the 32nd base pair segment
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*The [http://ada.org/ American Dental Association] cites it (together with omicron for "odont") as the symbol of dentistry.<ref>[http://ada.org/public/topics/emblem_dentistry.asp ADA.org: Oral Health Topics: Emblem/Insignia of Dentistry]{{dead link|date=September 2010}}</ref>
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===Lower case===
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The lower-case letter δ can be used to denote
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*An [[differential (infinitesimal)|infinitesimal change]] in the value of a variable in [[infinitesimal calculus]]
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*An auxiliary function in [[Calculus]] used to rigorously define the [[Limit of a function|limit]] or [[Continuous function|continuity]] of a given function.
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*The [[Kronecker delta]] in mathematics
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*The [[Dirac delta function]] in mathematics
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*The transition function in [[Finite state machine|automata]]
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*[[Deflection (engineering)|Deflection]] in engineering mechanics
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*The [[Compound interest|Force of Interest]] in actuarial science
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*The [[chemical shift]] of [[Nuclear Magnetic Resonance]] in chemistry
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*The relative [[electronegativity]] of different atoms in a molecule, δ<sup>&minus;</sup> being more electronegative than δ<sup>+</sup>
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*Text requiring deletion in [[proofreading]]. The usage is said to date back to classical times
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*In some of the manuscripts written by Dr. [[John Dee (mathematician)|John Dee]], the character of delta is used to represent Dee
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*The Computer Science chapter at the [[Royal Institute of Technology]]<ref>{{cite web|url=http://www.d.kth.se/sektionen/formalia/stadgar/#paragraf2.2 |title=Konglig Datasektionen, Statutes, §2.2 Symbol |publisher=D.kth.se |date= |accessdate=2010-09-07}}</ref>
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*Is a subunit of the F1 sector of the [[F-ATPase]]
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*The [[declination]] of an object in the [[equatorial coordinate system]] of [[astronomy]]
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*The dividend yield on the [[Black-Scholes]] option pricing formula
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*Signifies a major seventh chord in jazz music notation.
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*Ratios of [[environmental isotopes]], such as <sup>18</sup>O/<sup>16</sup>O and [[Deuterium|D]]/<sup>1</sup>H from waters are displayed using [[Isotope geochemistry|delta notation]] - δ<sup>18</sup>O and δD, respectively
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*The rate of depreciation of the aggregate capital stock of an economy in an [[exogenous growth model]] in [[macroeconomics]].<ref>[http://economics.mit.edu/kevinnguyen ]{{dead link|date=July 2010}}</ref>
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==See also==
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*[[D|D, d]]
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*[[De (Cyrillic)|Д, д]]
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*[[Th (digraph)|Th]]
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*[[Greek letters used in mathematics, science, and engineering]]
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*[[Nabla symbol]] (<math>\nabla</math>)
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*[[∂]] - the [[partial derivative]] symbol, sometimes mistaken for a lowercase Greek letter Delta.
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==References==
[[Category:Greek letters]]
[[Category:Greek letters]]

Revision as of 14:48, 31 January 2011

Delta (uppercase Δ, lowercase δ; δέλτα{{#if:| 

|[[Category:Articles containing {{#switch:el
 |ar       = Arabic
 |es       = Spanish
 |de       = German
 |fr       = French
 |ja       = Japanese
 |zh       = Chinese
 |bg       = Bulgarian
 |cs       = Czech
 |da       = Danish
 |nl       = Dutch
 |et       = Estonian
 |fi       = Finnish
 |el       = Greek
 |hu       = Hungarian
 |ga       = Irish
 |grc      = Ancient Greek
 |la|lat   = Latin
 |cy       = Welsh
 |en|eng   = explicitly cited English 
 |#default = {{#ifexist:Category:Articles containing Template:ISO 639 name el language text
  |Template:ISO 639 name el
  |non-English
 }}
}} language text]]

}}; 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).

Contents

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
<math>\Delta f = \sum_{i=1}^n {\frac{\partial^2 f}{\partial x_i^2}}</math>
<math>\Delta = b^2 - 4ac\,\!</math>

Lower case

The lower-case letter δ can be used to denote

|CitationClass=web }}</ref>

See also

References

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