Editing Delta (letter) (section)

==Uppercase==
The uppercase letter Δ is used to denote:
* Change of any changeable quantity, in mathematics and the sciences (in particular, the [[difference operator]]<ref name="Richardson1954">{{cite book
|author=Clarence H. Richardson
|title=''An Introduction to the Calculus of Finite Differences''
|url=https://archive.org/details/introductiontoca00rich
|url-access=registration
|year=1954
|publisher=Van Nostrand
|at=Chapter 1, pp. 1—3}}[http://babel.hathitrust.org/cgi/pt?id=mdp.39015000982945;view=1up;seq=5 online copy]</ref><ref name="Comenetz2002">{{cite book
|author=Michael Comenetz
|title=Calculus: The Elements
|year=2002
|publisher=World Scientific
|isbn=978-981-02-4904-5
|pages=73–74}}</ref>); for example, in <math>
\frac{y_2-y_1}{x_2-x_1}=\frac{\Delta y}{\Delta x}
</math>, 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 {{lang|el|διαφορά}}, ''diaphorá'', "difference". (The small [[Latin]] letter '''d''' is used in much the same way for the notation of [[derivative]]s and [[differential (mathematics)|differentials]], which also describe change by [[infinitesimal]] amounts.)
* The [[Laplace operator]]:
*: <math>\Delta f=\sum_{i=1}^n{\frac{\partial^2f}{\partial x_i^2}}</math>.
* The [[discriminant]] of a [[polynomial]] equation, especially the [[quadratic equation]]:<ref>{{cite book
|title=Solving polynomial equations: foundations, algorithms, and applications
|first1=Alicia
|last1=Dickenstein
|author1-link=Alicia Dickenstein
|first2=Ioannis Z.
|last2=Emiris
|publisher=Springer
|year=2005
|isbn=978-3-540-24326-7
|url=https://books.google.com/books?id=rSs-pQNrO_YC&pg=PA26
|at=Example 2.5.6, p. 120}}
</ref><ref>{{cite book
|title=Integers, polynomials, and rings
|first1=Ronald S.
|last1=Irving
|publisher=Springer-Verlag New York, Inc.
|year=2004
|isbn=978-0-387-40397-7
|url=https://books.google.com/books?id=B4k6ltaxm5YC&pg=PA154
|at=Ch. 10.1, pp. 145}}</ref>
*: <math>\Delta=b^2-4ac</math>.
* The [[area of a triangle]]:
*: <math>\Delta=\tfrac{1}{2}ab\sin{C}</math>.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Triangle Area |url=https://mathworld.wolfram.com/TriangleArea.html |access-date=2025-01-23 |website=mathworld.wolfram.com |language=en}}</ref>
* The [[symmetric difference]] of two sets.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Symmetric Difference |url=https://mathworld.wolfram.com/SymmetricDifference.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en |quote=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.}}</ref>
* A [[derivative|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 baryon|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 [[isomer]]ic forms.
* A [[simplex]], [[simplicial complex]], or [[convex hull]].
* In chemistry, the addition of heat in a reaction.
* In [[legal shorthand]], it represents a [[defendant]].<ref>{{cite book |last1=Tepper |first1=Pamela |url=https://books.google.com/books?id=z9wbCgAAQBAJ |title=The Law of Contracts and the Uniform Commercial Code |publisher=Cengage Learning |year=2014 |page=32 |isbn=978-1285448947 |access-date=2018-04-30 }}</ref>
* In the financial markets, one of the [[Greeks (finance)|Greeks]], describes the rate of change of an option price for a given change in the underlying benchmark.<ref>{{Cite web |title=Black-Scholes Formulas (d1, d2, Call Price, Put Price, Greeks) - Macroption |url=https://www.macroption.com/black-scholes-formula/ |access-date=2025-01-23 |website=www.macroption.com |quote=Delta is the first derivative of option price with respect to underlying price S.}}</ref>
* A [[major seventh chord]] in jazz music notation.<ref>{{Cite web |title=Every chord symbol found on lead sheets |url=https://jazz-library.com/articles/chord-symbols/ |access-date=2025-01-23 |website=Jazz-Library |language=en-US |quote=Chord with a triangle Major 7th “C△”}}</ref>
* In [[genetics]], it can stand for a [[Deletion (genetics)|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.<ref>{{cite web |url=http://www.ada.org/2517.aspx?currentTab=2 |title=Caduceus, the emblem of dentistry |website=American Dental Association |access-date=26 October 2017 |archive-url=https://web.archive.org/web/20121112073815/http://www.ada.org/2517.aspx?currentTab=2 |archive-date=12 November 2012 |url-status=dead}}</ref>
* The anonymous signature of [[James David Forbes]].<ref>[[Proceedings of the Royal Society]], vol. XIX, p. ii.</ref>
* Determinacy (having a definite truth-value) in [[philosophical logic]].<ref>{{Cite journal |last1=Shramko |first1=Yaroslav |last2=Wansing |first2=Heinrich |date=2010-03-30 |title=Truth Values |url=https://plato.stanford.edu/archIves/fall2015/entries/truth-values/}}</ref>
* In mathematics, the symbol ≜ (delta over equals) is occasionally used to define a new variable or function.<ref>{{cite web |url=https://hsm.stackexchange.com/questions/5166/who-first-defined-the-equal-delta-or-delta-over-equal-triangleq-symbol |title=Who first defined the "equal-delta" or "delta over equal" symbol? |access-date=2 October 2022 |archive-url=https://web.archive.org/web/20220306070901/https://hsm.stackexchange.com/questions/5166/who-first-defined-the-equal-delta-or-delta-over-equal-triangleq-symbol |archive-date=6 March 2022 |url-status=dead}}</ref>