Delta (letter)
Delta (uppercase Δ, lowercase δ or 𝛿; Δέλτα Délta; Modern Greek ) 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 .^{[1]} 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 uppercase letter delta (the shape is a triangle). Despite a popular legend, this use of the word delta was not coined by Herodotus.^{[2]}
Contents
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.
Upper case
The uppercase letter Δ can be used to denote:
 Change of any changeable quantity, in mathematics and the sciences (more specifically, the difference operator); for example, in:

 {y_2y_1\over x_2x_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 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.)
 The Laplace operator:
 \Delta f = \sum_{i=1}^n {\frac{\partial^2 f}{\partial x_i^2}}
 The discriminant of a polynomial equation, especially the quadratic equation:
 \Delta = b^2  4ac\,\!
 \Delta = \tfrac{1}{2} a b \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 (i.e. across a sample)
 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 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
 The symbol of the Greek inventor and architect Daedalus
 A major seventh chord in jazz music notation
 In genetics, it can stand for a gene deletion (e.g. the CCR5Δ32, 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.^{[3]}
 English indie rock band AltJ (so known because the symbol can be typed on a Mac OS X computer system by pressing AltJ.
 Often used as a symbol of homosexuality in the British gay community.
Lower case
The lowercase letter δ (or 𝛿) 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 Dirac delta function in mathematics
 In mathematics (specifically pointset topology), the boundary of a set A is denoted by δA .
 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 FATPase
 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 ^{18}O/^{16}O and D/^{1}H from water are displayed using delta notation – δ^{18}O and δD , respectively
 The rate of depreciation of the aggregate capital stock of an economy in an exogenous growth model in macroeconomics^{[4]}
 In a system that exhibits electrical reactance, the angle between voltage and current
Meteorology
 Delta was used as a name during the 1972 Atlantic hurricane season and the 2005 Atlantic hurricane season as Tropical Storm Delta (2005).
Keyboard Entry
On Microsoft Windows, a small delta can be generated by typing Alt+235. In certain programs (e.g. Microsoft Word), an uppercase delta can be typed using Alt+0916. However, in most other programs, Alt+0916 generates a closing quotation mark (”).
On OS X, optionj yields an uppercase delta (∆).
Computer encodings
 Greek Delta / Coptic Dalda
Character  Δ  δ  Ὗ  Ⲇ  

Unicode name  GREEK CAPITAL LETTER DELTA  GREEK SMALL LETTER DELTA  COPTIC CAPITAL LETTER DALDA  COPTIC SMALL LETTER DALDA  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  916  U+0394  948  U+03B4  8031  U+1F5F  11398  U+2C86 
UTF8  206 148  CE 94  206 180  CE B4  225 189 159  E1 BD 9F  226 178 134  E2 B2 86 
Numeric character reference  Δ  Δ  δ  δ  Ὗ  Ὗ  Ⲇ  Ⲇ 
Named character reference  Δ  δ  
DOS Greek  131  83  155  9B  
DOS Greek2  167  A7  221  DD  
Windows 1253  196  C4  228  E4  
TeX  \Delta  \delta 
 Latin Delta
Character  ẟ  ƍ  

Unicode name  LATIN SMALL LETTER DELTA  LATIN SMALL LETTER TURNED DELTA  
Encodings  decimal  hex  decimal  hex 
Unicode  7839  U+1E9F  397  U+018D 
UTF8  225 186 159  E1 BA 9F  198 141  C6 8D 
Numeric character reference  ẟ  ẟ  ƍ  ƍ 
 Technical and Mathematical symbols
Character  ∆  ∇  ≜  ⍋  ⍍  ⍙  

Unicode name  INCREMENT  NABLA  DELTA EQUAL TO  APL FUNCTIONAL SYMBOL DELTA STILE  APL FUNCTIONAL SYMBOL QUAD DELTA  APL FUNCTIONAL SYMBOL DELTA UNDERBAR  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  8710  U+2206  8711  U+2207  8796  U+225C  9035  U+234B  9037  U+234D  9049  U+2359 
UTF8  226 136 134  E2 88 86  226 136 135  E2 88 87  226 137 156  E2 89 9C  226 141 139  E2 8D 8B  226 141 141  E2 8D 8D  226 141 153  E2 8D 99 
Numeric character reference  ∆  ∆  ∇  ∇  ≜  ≜  ⍋  ⍋  ⍍  ⍍  ⍙  ⍙ 
Named character reference  ∇ 
 Mathematical Delta
Character  횫  훅  훥  훿  휟  휹  

Unicode name 
MATHEMATICAL BOLD CAPITAL DELTA 
MATHEMATICAL BOLD SMALL DELTA 
MATHEMATICAL ITALIC CAPITAL DELTA 
MATHEMATICAL ITALIC SMALL DELTA 
MATHEMATICAL BOLD ITALIC CAPITAL DELTA 
MATHEMATICAL BOLD ITALIC SMALL DELTA 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120491  U+1D6AB  120517  U+1D6C5  120549  U+1D6E5  120575  U+1D6FF  120607  U+1D71F  120633  U+1D739 
UTF8  240 157 154 171  F0 9D 9A AB  240 157 155 133  F0 9D 9B 85  240 157 155 165  F0 9D 9B A5  240 157 155 191  F0 9D 9B BF  240 157 156 159  F0 9D 9C 9F  240 157 156 185  F0 9D 9C B9 
UTF16  55349 57003  D835 DEAB  55349 57029  D835 DEC5  55349 57061  D835 DEE5  55349 57087  D835 DEFF  55349 57119  D835 DF1F  55349 57145  D835 DF39 
Numeric character reference  𝚫  𝚫  𝛅  𝛅  𝛥  𝛥  𝛿  𝛿  𝜟  𝜟  𝜹  𝜹 
Character  흙  흳  힓   

Unicode name 
MATHEMATICAL SANSSERIF BOLD CAPITAL DELTA 
MATHEMATICAL SANSSERIF BOLD SMALL DELTA 
MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL DELTA 
MATHEMATICAL SANSSERIF BOLD ITALIC SMALL DELTA 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120665  U+1D759  120691  U+1D773  120723  U+1D793  120749  U+1D7AD 
UTF8  240 157 157 153  F0 9D 9D 99  240 157 157 179  F0 9D 9D B3  240 157 158 147  F0 9D 9E 93  240 157 158 173  F0 9D 9E AD 
UTF16  55349 57177  D835 DF59  55349 57203  D835 DF73  55349 57235  D835 DF93  55349 57261  D835 DFAD 
Numeric character reference  𝝙  𝝙  𝝳  𝝳  𝞓  𝞓  𝞭  𝞭 
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.
See also
 D, d
 Д, д
 ẟ  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
References
 ^ http://www.merriamwebster.com/dictionary/delta
 ^
 ^ Caduceus, the emblem of dentistry  American Dental Association  ADA.org
 ^ http://econ.duke.edu/people?subpage=unit&Gurl=%2Faas%2FEconomics&cname=Masters+Students