Delta (letter)

Delta (uppercase Δ, lowercase δ; 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

• Change; e.g. in:

$\{y\_2-y\_1over\; x\_2-x\_1\}\; =\; \{Delta\; y\; over\; Delta\; x\}$ = the average change of y per unit x, i.e. the change of y over the change of x

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

$Delta\; f\; =\; sum\_\{i=1\}^n\; \{frac\{partial^2\; f\}\{partial\; x\_i^2\}\}$

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

$Delta\; =\; b^2\; -\; 4ac,!$

• 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
• A interval of possible values for a given quantity for instance across a sample
• 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.

The lower-case letter δ

• An infinitesimal change in the value of a variable in mathematics or science
• 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
• Is a subunit of the F1 sector of the F-ATPase

See also

• Greek letters used in mathematics, science, and engineering
• D, d - Latin
• Д, д (Д, д) - De (Cyrillic)
• Th - Digraph

References