Vinculum (symbol)

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A vinculum is a horizontal line placed over a mathematical expression, used to indicate that it is to be considered a group. Vinculum is Latin for "bond", "fetter", "chain", or "tie", which is roughly suggestive of some of the uses of the symbol.

Examples of its use include the case of a group of infinitely repeating decimal digits, for example,

$\frac{1}{3} = 0.333333\dots = 0.\overline{3}.$

It is also used in the notation of a radical to indicate the radicand whose root is being indicated. In the next case, the quantity $a b + 2$ is the radicand, and thus has a vinculum over it.

$\sqrt[n]{ab+2}$

It is also used to show the repeating terms in a periodic continued fraction. Quadratic irrational numbers are the only numbers that have these.

The vinculum is also sometimes used in Boolean algebra, where it serves to indicate a group of expressions whose logical result is to be negated, as in

$\overline{AB}.$

In particle physics, the vinculum is used to indicate antiparticles. For example, p and p are the symbols for proton and antiproton, respectively.

The vinculum should not be confused with a similar-looking vector notation, e.g. $\overrightarrow{AB}$ "vector from A to B", or $\vec{a}$ "vector named a".