Delta (letter)

For other uses, see Delta.

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 is used as the symbol for:

• The difference operator, affecting a change or difference between mathematical values:

${y_{2}-y_{1} \over x_{2}-x_{1}}={\Delta y \over \Delta x}$ = the average change of y per unit x commonly known as the change of y over the change of x.

• The Laplace operator:

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

• 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.
• As a symbol for defendant in legal shorthand.

The lower-case letter δ is used as the symbol for:

• An infinitesmal 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
• A mark for deletion in proofreading. The usage is said to date back to classical times.
• Indicating the electronegativity of different atoms in a molecule, δ^- being more electronegative than δ⁺.