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Delta (/ˈdɛltə/;[1] uppercase Δ, lowercase δ; Greek: δέλτα, délta, [ˈðelta])[2] 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 𐤃.[3] Letters that come from delta include Latin D and Cyrillic Д.
A river delta (originally, the delta of the Nile River) is so named 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.[4]
Pronunciation
[edit]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" or "this" (while IPA: [d] in foreign words is instead commonly transcribed as ντ). Delta is romanized as d or dh.
Uppercase
[edit]The uppercase letter Δ is used to denote:
- Change of any changeable quantity, in mathematics and the sciences (in particular, the difference operator[5][6]); for example, in 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:
- The discriminant of a polynomial equation, especially the quadratic equation:[7][8]
- The area of a triangle
- 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.[9]
- 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-Δ32, a 32 nucleotide/bp deletion within CCR5).
- The American Dental Association cites it (together with omicron for "odont") as the symbol of dentistry.[10]
- The anonymous signature of James David Forbes.[11]
- 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.[12]
Lowercase
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/NAMA_Alphabet_grec.jpg/220px-NAMA_Alphabet_grec.jpg)
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 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, 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[13]
- 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.[14]
- An Old Irish voiced dental or alveolar fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish dh
Computer encodings
[edit]- Greek Delta / Coptic Dalda
Preview | Δ | δ | ᵟ | Ⲇ | ⲇ | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL LETTER DELTA | GREEK SMALL LETTER DELTA | MODIFIER LETTER SMALL DELTA | COPTIC CAPITAL LETTER DALDA | COPTIC SMALL LETTER DALDA | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 916 | U+0394 | 948 | U+03B4 | 7519 | U+1D5F | 11398 | U+2C86 | 11399 | U+2C87 |
UTF-8 | 206 148 | CE 94 | 206 180 | CE B4 | 225 181 159 | E1 B5 9F | 226 178 134 | E2 B2 86 | 226 178 135 | E2 B2 87 |
Numeric character reference | Δ |
Δ |
δ |
δ |
ᵟ |
ᵟ |
Ⲇ |
Ⲇ |
ⲇ |
ⲇ |
Named character reference | Δ | δ | ||||||||
DOS Greek | 131 | 83 | 155 | 9B | ||||||
DOS Greek-2 | 167 | A7 | 221 | DD | ||||||
Windows 1253 | 196 | C4 | 228 | E4 | ||||||
TeX | \Delta | \delta |
Preview | ẟ | ƍ | ||
---|---|---|---|---|
Unicode name | LATIN SMALL LETTER DELTA | LATIN SMALL LETTER TURNED DELTA | ||
Encodings | decimal | hex | dec | hex |
Unicode | 7839 | U+1E9F | 397 | U+018D |
UTF-8 | 225 186 159 | E1 BA 9F | 198 141 | C6 8D |
Numeric character reference | ẟ |
ẟ |
ƍ |
ƍ |
- Technical and Mathematical symbols
Preview | ∆ | ∇ | ≜ | ⍋ | ⍍ | ⍙ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 8710 | U+2206 | 8711 | U+2207 | 8796 | U+225C | 9035 | U+234B | 9037 | U+234D | 9049 | U+2359 |
UTF-8 | 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
Preview | 𝚫 | 𝛅 | 𝛥 | 𝛿 | 𝜟 | 𝜹 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120491 | U+1D6AB | 120517 | U+1D6C5 | 120549 | U+1D6E5 | 120575 | U+1D6FF | 120607 | U+1D71F | 120633 | U+1D739 |
UTF-8 | 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 |
UTF-16 | 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 |
Preview | 𝝙 | 𝝳 | 𝞓 | 𝞭 | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL SANS-SERIF BOLD CAPITAL DELTA |
MATHEMATICAL SANS-SERIF BOLD SMALL DELTA |
MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL DELTA |
MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL DELTA | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120665 | U+1D759 | 120691 | U+1D773 | 120723 | U+1D793 | 120749 | U+1D7AD |
UTF-8 | 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 |
UTF-16 | 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
[edit]- Arrow (symbol)
- Chevron (insignia)
- ∆ (disambiguation)
- D, d
- Д, д
- ẟ - Latin delta
- ∂ - the partial derivative symbol, a curved d, 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)
- Thorn (letter)
- Greek letters used in mathematics, science, and engineering
- ∇ - Nabla symbol
- Delta Air Lines
- SARS-CoV-2 Delta variant
References
[edit]- ^ "delta". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ "Dictionary of Standard Modern greek". Centre for the Greek Language.
- ^ "Definition of DELTA". www.merriam-webster.com. Retrieved 26 October 2017.
- ^ Celoria, Francis (1966). "Delta as a geographical concept in Greek literature". Isis. 57 (3): 385–388. doi:10.1086/350146. JSTOR 228368. S2CID 143811840.
- ^ Clarence H. Richardson (1954). An Introduction to the Calculus of Finite Differences. Van Nostrand. Chapter 1, pp. 1—3.online copy
- ^ Michael Comenetz (2002). Calculus: The Elements. World Scientific. pp. 73–74. ISBN 978-981-02-4904-5.
- ^ Dickenstein, Alicia; Emiris, Ioannis Z. (2005). Solving polynomial equations: foundations, algorithms, and applications. Springer. Example 2.5.6, p. 120. ISBN 978-3-540-24326-7.
- ^ Irving, Ronald S. (2004). Integers, polynomials, and rings. Springer-Verlag New York, Inc. Ch. 10.1, pp. 145. ISBN 978-0-387-40397-7.
- ^ Tepper, Pamela (2014). The Law of Contracts and the Uniform Commercial Code. Cengage Learning. p. 32. ISBN 978-1285448947. Retrieved 2018-04-30.
- ^ "Caduceus, the emblem of dentistry". American Dental Association. Archived from the original on 12 November 2012. Retrieved 26 October 2017.
- ^ Proceedings of the Royal Society, vol. XIX, p. ii.
- ^ "Who first defined the "equal-delta" or "delta over equal" symbol?". Archived from the original on 6 March 2022. Retrieved 2 October 2022.
- ^ "Faculty - Economics Department". econ.duke.edu. Retrieved 26 October 2017.
- ^ MACHADO, Fábio Braz, NARDY, Antônio José Ranalli (2018). Mineralogia Óptica. São Paulo: Oficina de Textos. p. 85. ISBN 9788579752452.
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