Delta

Look up Δ or δ in Wiktionary, the free dictionary.

Greek alphabet
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
Obsolete letters
	Digamma		Qoppa
	San		Sampi
Other characters
	Stigma		Sho
	Heta
Greek diacritics

Delta (uppercase Δ, lowercase δ; Greek: Δέλτα [ðelta] Thelta) 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, but in the Ancient Greek language, it represented a voiced dental plosive /d̪/.

A river delta is so named because its shape approximates the upper-case letter delta.

The upper-case letter Δ

The upper-case letter Δ can be used to denote

• Change; e.g. in

, the average change of y per unit x, i.e. the change of y over the change of x

• More specifically, the difference operator.
• The Laplace operator:

• The discriminant of a polynomial equation, especially the quadratic equation:

• A macroscopic change in the value of a variable in mathematics or science
• Uncertainty in a physical variable as seen in for instance the uncertainty principle
• An interval of possible values for a given quantity for instance across a sample^{[citation needed]}
• 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
• In legal shorthand, it represents a defendant
• In the financial markets, it is one of the Greeks that describes the rate of change of an option price for a given change in the underlying benchmark
• In genetics, it can stand for a gene deletion, e.g. the CCR5-Δ32 a deletion of the CCR5 at the 32nd bp segment
• In chemistry, it denotes the change in a physical property such as heat, e.g. ΔTemp would stand for the change in Temp
• The American Dental Association cites it (together with omicron for "odont") as the symbol of dentistry. ^[1]

The lower-case letter δ

The lower-case letter δ can be used to denote

• An infinitesimal change in the value of a variable in infinitesimal calculus
• An auxiliary function in Calculus used to rigorously define the limit or continuity of a given function.
• The Kronecker delta in mathematics
• 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
• The Computer Science chapter at the Royal Institute of Technology^[2]
• Is 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 on the Black-Scholes option pricing formula
• Ratios of environmental isotopes, such as ¹⁸O/¹⁶O and D/¹H from waters are displayed using delta notation - δ¹⁸O and δD, respectively.

See also

• D, d
• Д, д
• Th
• Greek letters used in mathematics, science, and engineering
• Nabla symbol ()

References

1. ^ ADA.org: Oral Health Topics: Emblem/Insignia of Dentistry
2. ^ Konglig Datasektionen, Statutes, §2.2 Symbol