Movatterモバイル変換

Jump to content

Delta (letter)

From Wikipedia, the free encyclopedia

(Redirected fromDelta (Greek letter))

Fourth letter in the Greek alphabet

"Δ" redirects here. For other uses, see∆ (disambiguation).

Not to be confused with ẟ, theLatin delta.

This articleneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "Delta" letter – news ·newspapers ·books ·scholar ·JSTOR(February 2015) (Learn how and when to remove this message)

Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega

Archaic local variants

Ϝϝ	Digamma	Ͱͱ	Heta
Ϻϻ	San	Ϙϙ	Koppa
Ͷͷ	Tsan Digamma	Ͳͳ	Sampi
Ϸϸ	Sho

Diacritics and other symbols

Numerals (Attic)

Related topics

Category

v
t
e

Delta (/ˈdɛltə/ ^ⓘDEL-tə;^[1] uppercaseΔ, lowercaseδ;Greek:δέλτα,délta,[ˈðelta])^[2] is the fourth letter of theGreek alphabet. In the system ofGreek numerals, it has a value of four. It was derived from thePhoenician letter dalet 𐤃.^[3] Letters that come from delta include theLatin D and theCyrillic Д.

Ariver delta (originally, thedelta of theNile River) is named so because its shape approximates the triangular uppercase letter delta. Contrary to a popular legend,^[vague] this use of the worddelta was not coined byHerodotus.^[4]

Pronunciation

InAncient Greek, delta represented avoiced dental plosiveIPA:[d]. InModern Greek, it represents avoiced dental fricativeIPA:[ð], like the "th" in "that" or "this" (whileIPA:[d] in foreign words is instead commonly transcribed as ντ). Delta isromanized asd ordh.

Uppercase

The uppercase letter Δ is used to denote:

Change of any changeable quantity, in mathematics and the sciences (in particular, thedifference operator^[5]^[6]); for example, in ${\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {\Delta y}{\Delta x}}$ , the average change ofy per unitx (i.e. the change ofy over the change ofx). Delta is the initial letter of the Greek wordδιαφορά,diaphorá, "difference". (The smallLatin letterd is used in much the same way for the notation ofderivatives anddifferentials, which also describe change byinfinitesimal amounts.)
TheLaplace operator:
$\Delta f=\sum _{i=1}^{n}{\frac {\partial ^{2}f}{\partial x_{i}^{2}}}$ .
Thediscriminant of apolynomial equation, especially thequadratic equation:^[7]^[8]
$\Delta =b^{2}-4ac$ .
Thearea of a triangle:
$\Delta ={\tfrac {1}{2}}ab\sin {C}$ .^[9]
Thesymmetric difference of two sets.^[10]
Amacroscopic change in the value of a variable in mathematics or science.
Uncertainty in a physical variable as seen in theuncertainty principle.
An interval of possible values for a given quantity.
Any of thedelta particles in particle physics.
The determinant of the matrix of coefficients of a set of linear equations (seeCramer's rule).
That an associatedlocant number represents the location of acovalent bond in anorganic compound, the position of which is variant betweenisomeric forms.
Asimplex,simplicial complex, orconvex hull.
In chemistry, the addition of heat in a reaction.
Inlegal shorthand, it represents adefendant.^[11]
In the financial markets, one of theGreeks, describes the rate of change of an option price for a given change in the underlying benchmark.^[12]
Amajor seventh chord in jazz music notation.^[13]
Ingenetics, it can stand for agene deletion (e.g. theCCR5-Δ32, a 32 nucleotide/bp deletion within CCR5).
TheAmerican Dental Association cites it (together withomicron for "odont") as the symbol of dentistry.^[14]
The anonymous signature ofJames David Forbes.^[15]
Determinacy (having a definite truth-value) inphilosophical logic.^[16]
In mathematics, the symbol ≜ (delta over equals) is occasionally used to define a new variable or function.^[17]

Lowercase

Thealphabet on ablack figure vessel, with a D-shaped delta.

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

A change in the value of a variable incalculus.
Afunctional derivative infunctional calculus.
The(ε, δ)-definition of limits, in mathematics and more specifically incalculus.^[18]
TheKronecker delta in mathematics.^[19]
Thecentral difference for a function.^[20]
The degree of avertex ingraph theory.
TheDirac delta function in mathematics.^[21]
The transition function inautomata.
Deflection in engineering mechanics.
Theforce of interest in actuarial science.
Thechemical shift ofnuclear magnetic resonance in chemistry.
The relativeelectronegativity of different atoms in a molecule, δ⁻ being more electronegative than δ⁺.
Text requiring deletion inproofreading; 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.^[22]
A subunit of the F1 sector of theF-ATPase.
Thedeclination of an object in theequatorial coordinate system ofastronomy.^[23]
The dividend yield in theBlack–Scholes option pricing formula.
Ratios ofenvironmental isotopes, such as¹⁸O/¹⁶O andD/¹H from water are displayed usingdelta notation –δ¹⁸O andδD, respectively.
The rate of depreciation of the aggregate capital stock of an economy in anexogenous growth model inmacroeconomics.^[24]
In a system that exhibitselectrical reactance, the angle betweenvoltage andcurrent.
Partial charge in chemistry.^[25]
The maximumbirefringence of a crystal inoptical mineralogy.^[26]
AnOld Irish voiced dental or alveolarfricative of uncertain articulation, the ancestor of the sound represented byModern Irishdh.
Silver ratio^[27]

Unicode

U+018D ƍLATIN SMALL LETTER TURNED DELTA
U+0394 ΔGREEK CAPITAL LETTER DELTA (Δ) (\Delta in TeX)
U+03B4 δGREEK SMALL LETTER DELTA (δ) (\delta in TeX)
U+1D5F ᵟMODIFIER LETTER SMALL DELTA
U+1E9F ẟLATIN SMALL LETTER DELTA
U+2207 ∇NABLA (&Del;, ∇)
U+225C ≜DELTA EQUAL TO (&triangleq;, &trie;)
U+234B ⍋APL FUNCTIONAL SYMBOL DELTA STILE
U+234D ⍍APL FUNCTIONAL SYMBOL QUAD DELTA
U+2359 ⍙APL FUNCTIONAL SYMBOL DELTA UNDERBAR
U+2C86 ⲆCOPTIC CAPITAL LETTER DALDA
U+2C87 ⲇCOPTIC SMALL LETTER DALDA
U+1D6AB 𝚫MATHEMATICAL BOLD CAPITAL DELTA^[a]
U+1D6C5 𝛅MATHEMATICAL BOLD SMALL DELTA
U+1D6E5 𝛥MATHEMATICAL ITALIC CAPITAL DELTA
U+1D6FF 𝛿MATHEMATICAL ITALIC SMALL DELTA
U+1D71F 𝜟MATHEMATICAL BOLD ITALIC CAPITAL DELTA
U+1D739 𝜹MATHEMATICAL BOLD ITALIC SMALL DELTA
U+1D759 𝝙MATHEMATICAL SANS-SERIF BOLD CAPITAL DELTA
U+1D773 𝝳MATHEMATICAL SANS-SERIF BOLD SMALL DELTA
U+1D793 𝞓MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL DELTA
U+1D7AD 𝞭MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL DELTA

^TheMATHEMATICAL codes should only be used in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

Look upΔ orδ in Wiktionary, the free dictionary.

Arrow (symbol)
Chevron (insignia)
∆ (disambiguation)
D, d
Д, д
ẟ – Latin delta
∂ – thepartial derivative symbol, a curvedd, sometimes mistaken for a lowercase Greek letter Delta.
ð – the smalleth appears similar to a small delta and also represents ad 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

^"delta".Oxford English Dictionary (Online ed.).Oxford University Press. (Subscription orparticipating institution membership required.)
^"Dictionary of Standard Modern greek". Centre for the Greek Language.
^"Definition of DELTA".www.merriam-webster.com. Retrieved26 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.
^Weisstein, Eric W."Triangle Area".mathworld.wolfram.com. Retrieved2025-01-23.
^Weisstein, Eric W."Symmetric Difference".mathworld.wolfram.com. Retrieved2025-01-31.The symmetric difference of sets A and B is variously written as A ⊖ B, A∇ B, A+B (Borowski and Borwein 1991) or AΔB (Harris and Stocker 1998, p. 3). All but the first notation should probably be deprecated since each of the other symbols has a common meaning in other areas of mathematics.
^Tepper, Pamela (2014).The Law of Contracts and the Uniform Commercial Code. Cengage Learning. p. 32.ISBN 978-1285448947. Retrieved2018-04-30.
^"Black-Scholes Formulas (d1, d2, Call Price, Put Price, Greeks) - Macroption".www.macroption.com. Retrieved2025-01-23.Delta is the first derivative of option price with respect to underlying price S.
^"Every chord symbol found on lead sheets".Jazz-Library. Retrieved2025-01-23.Chord with a triangle Major 7th "C△"
^"Caduceus, the emblem of dentistry".American Dental Association. Archived fromthe original on 12 November 2012. Retrieved26 October 2017.
^Proceedings of the Royal Society, vol. XIX, p. ii.
^Shramko, Yaroslav; Wansing, Heinrich (2010-03-30)."Truth Values".{{cite journal}}:Cite journal requires|journal= (help)
^"Who first defined the "equal-delta" or "delta over equal" symbol?". Archived fromthe original on 6 March 2022. Retrieved2 October 2022.
^Weisstein, Eric W."Epsilon-Delta Proof".mathworld.wolfram.com. Retrieved2025-01-31.
^Weisstein, Eric W."Kronecker Delta".mathworld.wolfram.com. Retrieved2025-01-23.
^Weisstein, Eric W."Central Difference".mathworld.wolfram.com. Retrieved2025-01-31.
^Weisstein, Eric W."Delta Function".mathworld.wolfram.com. Retrieved2025-01-23.
^"Greek Alphabet".Ancient Symbols. Retrieved2025-01-31.Dr. John Dee, a mathematician, used the lowercase Delta symbol to represent himself in manuscripts.
^"Greek Alphabet".Ancient Symbols. Retrieved2025-01-31.In astronomy, the symbol is used to represent the declination of an object.
^"Faculty - Economics Department".econ.duke.edu. Retrieved26 October 2017.
^"Declination",The Encyclopedia of Astronomy and Astrophysics, IOP Publishing Ltd, 2001,doi:10.1888/0333750888/4541,ISBN 0-333-75088-8, retrieved2025-01-31
^MACHADO, Fábio Braz, NARDY, Antônio José Ranalli (2018).Mineralogia Óptica. São Paulo: Oficina de Textos. p. 85.ISBN 9788579752452.{{cite book}}: CS1 maint: multiple names: authors list (link)
^Weisstein, Eric W."Silver Ratio".mathworld.wolfram.com. Retrieved2025-01-31.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Delta_(letter)&oldid=1282617831"

Greek letters

Hidden categories:

[8]ページ先頭

©2009-2025 Movatter.jp