DELTA (LETTER)

'Delta' (upside down 'A', uppercase 'Δ', lowercase 'δ') 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 . Letters that arose from Delta include the Latin D and the equivalent in the Cyrillic alphabet Д.
In Modern Greek it represents a voiced dental fricative , (like the th in the English word ''th''is) but in the Ancient Greek language, it represented a voiced dental plosive .
A river delta is named after the letter delta because it has roughly the triangular shape of the upper-case delta.
The upper-case letter Δ can be used to denote:

★ The difference operator, effecting a change or difference between mathematical values:
:$\{y\_2-y\_1over\; x\_2-x\_1\}\; =\; \{Delta\; y\; over\; Delta\; x\}$ = the average change of y per unit x commonly known as the change of y over the change of x.

★ By extension of the above, change generally, a use which shows up frequently in medical charts.

★ The Laplace operator:
:

★ The discriminant of the quadratic equation:
:$Delta\; =\; b^2\; -\; 4ac,!$

★ A macroscopic change in the value of a variable in mathematics or science.

★ Any of the delta particles in particle physics.

★ 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 genetics, it can stand for a gene deletion, e.g. the CCR5-Δ32 a deletion of the CCR5 at the 32nd bp segment.

★ In medical shorthand, it can stand for change of any type.
The lower-case letter δ can be used to denote:

★ 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.

★ Deflection in engineering mechanics

★ Text requiring deletion in proofreading. The usage is said to date back to classical times.

★ The relative electronegativity of different atoms in a molecule, δ⁻ being more electronegative than δ⁺.

★ In some of the manuscripts written by Dr. John Dee, the character of delta is used to represent Dee.

★ The transition function in automata.