Ðelta or Delta (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 /ð/, (like the th in the English word this) but in the Ancient Greek language, it represented a voiced dental plosive [d]. 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:
- <math>{y_2-y_1\over x_2-x_1} = {\Delta y \over \Delta x} </math> = 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:
- <math>\Delta f = \sum_{i=1}^n {\frac{\partial^2 f}{\partial x_i^2}} </math>
- The discriminant of a polynomial equation, especially the quadratic equation:
- <math>\Delta = b^2 - 4ac\,\!</math>
- 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 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 medical shorthand, it can stand for change of any type.
- In chemistry, it denotes energy in the form of heat.
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
- The Force of Interest in actuarial science.
- 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.
- The Computer Science chapter at the Royal Institute of Technology. [1]
