Delta (letter)
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Delta Letter

Delta [1] (uppercase ?, lowercase ? or ?; Greek: délta, ['ðelta][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 ?,[3] 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 triangular uppercase letter delta. Contrary to a popular legend, this use of the word delta was not coined by Herodotus.[4]

## 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" (while /d/ in foreign words is instead commonly transcribed as ). Delta is romanized as d or dh.

## Upper case

The uppercase letter ? is used to denote:

${\displaystyle {y_{2}-y_{1} \over x_{2}-x_{1}}={\Delta y \over \Delta x},}$
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.)
${\displaystyle \Delta f=\sum _{i=1}^{n}{\frac {\partial ^{2}f}{\partial x_{i}^{2}}}}$
${\displaystyle \Delta =b^{2}-4ac\,\!}$
${\displaystyle \Delta ={\tfrac {1}{2}}ab\sin {C}}$

## Lower case

The alphabet on a black figure vessel, with a D-shaped delta.

The lowercase letter ? (or ?) can be used to denote:

## Computer encodings

• Greek Delta / Coptic Dalda
Character information
Preview Δ δ
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 decimal hex decimal hex decimal hex decimal 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 &#916; &#x394; &#948; &#x3B4; &#7519; &#x1D5F; &#11398; &#x2C86; &#11399; &#x2C87;
Named character reference &Delta; &delta;
DOS Greek 131 83 155 9B
DOS Greek-2 167 A7 221 DD
Windows 1253 196 C4 228 E4
TeX \Delta \delta
• Latin Delta
Character information
Preview ƍ
Unicode name LATIN SMALL LETTER DELTA LATIN SMALL LETTER TURNED DELTA
Encodings decimal hex decimal hex
Unicode 7839 U+1E9F 397 U+018D
UTF-8 225 186 159 E1 BA 9F 198 141 C6 8D
Numeric character reference &#7839; &#x1E9F; &#397; &#x18D;
• Technical and Mathematical symbols
Character information
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 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
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 &#8710; &#x2206; &#8711; &#x2207; &#8796; &#x225C; &#9035; &#x234B; &#9037; &#x234D; &#9049; &#x2359;
Named character reference &Del;, &nabla; &triangleq;, &trie;
• Mathematical Delta
Character information
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 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
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 &#120491; &#x1D6AB; &#120517; &#x1D6C5; &#120549; &#x1D6E5; &#120575; &#x1D6FF; &#120607; &#x1D71F; &#120633; &#x1D739;
Character information
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 decimal hex decimal hex decimal 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 &#120665; &#x1D759; &#120691; &#x1D773; &#120723; &#x1D793; &#120749; &#x1D7AD;

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.

## References

1. ^ "delta". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.)
2. ^ "Dictionary of Standard Modern greek". Centre for the Greek Language.
3. ^ "Definition of DELTA". www.merriam-webster.com. Retrieved 2017.
4. ^ Celoria, Francis (1966). "Delta as a geographical concept in Greek literature". Isis. 57 (3): 385-388. doi:10.1086/350146. JSTOR 228368.
5. ^ Clarence H. Richardson (1954). An Introduction to the Calculus of Finite Differences. Van Nostrand. Chapter 1, pp. 1--3.online copy
6. ^ Michael Comenetz (2002). Calculus: The Elements. World Scientific. pp. 73-74. ISBN 978-981-02-4904-5.
7. ^ 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.
8. ^ Irving, Ronald S. (2004). Integers, polynomials, and rings. Springer-Verlag New York, Inc. Ch. 10.1, pp. 145. ISBN 978-0-387-40397-7.
9. ^ Tepper, Pamela (2014). The Law of Contracts and the Uniform Commercial Code. Cengage Learning. p. 32. ISBN 978-1285448947. Retrieved .
10. ^ "Caduceus, the emblem of dentistry - American Dental Association - ADA.org". Archived from the original on 12 November 2012. Retrieved 2017.
11. ^ Proceedings of the Royal Society, vol. XIX, p ii
12. ^ "Faculty - Economics Department". econ.duke.edu. Retrieved 2017.
13. ^ MACHADO, Fábio Braz, NARDY, Antônio José Ranalli (2018). Mineralogia Óptica. São Paulo: Oficina de Textos. p. 85. ISBN 9788579752452.