Vinculum (symbol)

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,

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

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 $ab+2$ 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 Overline|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".

External links

*MathWorld|urlname=PeriodicContinuedFraction|title=Periodic Continued Fraction
*MathWorld|urlname=Vinculum|title=Vinculum