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 "chain", reflecting the function of the symbol.

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

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

It is also used in common arithmetic to denote that the numerator is being divided by the denominator as a whole group.

\frac{500}{10 \times 10} = \frac{5}{1} = 5

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}

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: [Periodic Continued Fraction]

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