# Delta (letter)

Delta (uppercase Δ, lowercase δ or 𝛿; Greek: δέλτα délta, [ˈðelta][1]) 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,[2] 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 triangular uppercase letter delta. Despite a popular legend, this use of the word delta was not coined by Herodotus.[3]

## 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:

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

## Lower case

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

## Computer encodings

• Greek Delta / Coptic Dalda
CharacterΔδ
Unicode nameGREEK CAPITAL LETTER DELTAGREEK SMALL LETTER DELTAMODIFIER LETTER SMALL DELTACOPTIC CAPITAL LETTER DALDACOPTIC SMALL LETTER DALDA
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode916U+0394948U+03B47519U+1D5F11398U+2C8611399U+2C87
UTF-8206 148CE 94206 180CE B4225 181 159E1 B5 9F226 178 134E2 B2 86226 178 135E2 B2 87
Numeric character reference&#916;&#x394;&#948;&#x3B4;&#7519;&#x1D5F;&#11398;&#x2C86;&#11399;&#x2C87;
Named character reference&Delta;&delta;
DOS Greek131831559B
DOS Greek-2167A7221DD
Windows 1253196C4228E4
TeX\Delta\delta
• Latin Delta
Characterƍ
Unicode nameLATIN SMALL LETTER DELTALATIN SMALL LETTER TURNED DELTA
Encodingsdecimalhexdecimalhex
Unicode7839U+1E9F397U+018D
UTF-8225 186 159E1 BA 9F198 141C6 8D
Numeric character reference&#7839;&#x1E9F;&#397;&#x18D;
• Technical and Mathematical symbols
Character
Unicode nameINCREMENTNABLADELTA EQUAL TOAPL FUNCTIONAL SYMBOL DELTA STILEAPL FUNCTIONAL SYMBOL QUAD DELTAAPL FUNCTIONAL SYMBOL DELTA UNDERBAR
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode8710U+22068711U+22078796U+225C9035U+234B9037U+234D9049U+2359
UTF-8226 136 134E2 88 86226 136 135E2 88 87226 137 156E2 89 9C226 141 139E2 8D 8B226 141 141E2 8D 8D226 141 153E2 8D 99
Numeric character reference&#8710;&#x2206;&#8711;&#x2207;&#8796;&#x225C;&#9035;&#x234B;&#9037;&#x234D;&#9049;&#x2359;
Named character reference&nabla;
• Mathematical Delta
Character𝚫𝛅𝛥𝛿𝜟𝜹
Unicode nameMATHEMATICAL 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
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120491U+1D6AB120517U+1D6C5120549U+1D6E5120575U+1D6FF120607U+1D71F120633U+1D739
UTF-8240 157 154 171F0 9D 9A AB240 157 155 133F0 9D 9B 85240 157 155 165F0 9D 9B A5240 157 155 191F0 9D 9B BF240 157 156 159F0 9D 9C 9F240 157 156 185F0 9D 9C B9
UTF-1655349 57003D835 DEAB55349 57029D835 DEC555349 57061D835 DEE555349 57087D835 DEFF55349 57119D835 DF1F55349 57145D835 DF39
Numeric character reference&#120491;&#x1D6AB;&#120517;&#x1D6C5;&#120549;&#x1D6E5;&#120575;&#x1D6FF;&#120607;&#x1D71F;&#120633;&#x1D739;
Character𝝙𝝳𝞓𝞭
Unicode nameMATHEMATICAL 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
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
UTF-8240 157 157 153F0 9D 9D 99240 157 157 179F0 9D 9D B3240 157 158 147F0 9D 9E 93240 157 158 173F0 9D 9E AD
UTF-1655349 57177D835 DF5955349 57203D835 DF7355349 57235D835 DF9355349 57261D835 DFAD

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. "Dictionary of Standard Modern greek". Centre for the Greek Language.
2. "Definition of DELTA". www.merriam-webster.com. Retrieved 26 October 2017.
3. Celoria, Francis (1966). "Delta as a geographical concept in Greek literature". Isis. 57 (3): 385–388. doi:10.1086/350146. JSTOR 228368.
4. Clarence H. Richardson (1954). An Introduction to the Calculus of Finite Differences. Van Nostrand. Chapter 1, pp. 1—3.online copy
5. Michael Comenetz (2002). Calculus: The Elements. World Scientific. pp. 73–74. ISBN 978-981-02-4904-5.
6. 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.
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.
8. Tepper, Pamela (2014). The Law of Contracts and the Uniform Commercial Code. Cengage Learning. p. 32. ISBN 978-1285448947. Retrieved 2018-04-30.
9. "Caduceus, the emblem of dentistry - American Dental Association - ADA.org". Archived from the original on 12 November 2012. Retrieved 26 October 2017.
10. Proceedings of the Royal Society, vol. XIX, p ii
11. "Faculty - Economics Department". econ.duke.edu. Retrieved 26 October 2017.
12. MACHADO, Fábio Braz, NARDY, Antônio José Ranalli (2018). Mineralogia Óptica. São Paulo: Oficina de Textos. p. 85. ISBN 9788579752452.