Vinculum (symbol)
A vinculum is a horizontal line used in mathematical notation for a specific purpose. It is most commonly used today to indicate the repetend of a repeating decimal. It may be placed as an overline (or underline) over (under) a mathematical expression to indicate that the expression is to be considered grouped together. For most of its uses it has been replaced by parentheses in modern notational style.
Vinculum is Latin for "bond", "fetter", "chain", or "tie", which is suggestive of some of the uses of the symbol.
A vinculum can indicate a line segment where A and B are the endpoints:
A vinculum can indicate the repetend of a repeating decimal value:
Similarly, it is used to show the repeating terms in a periodic continued fraction. Quadratic irrational numbers are the only numbers that have these.
Its main use was as a notation to indicate a group (a bracketing device serving the same function as parentheses):
meaning to add b and c first and then subtract the result from a, which would be written more commonly today as a − (b + c). Parentheses, used for grouping, are only rarely found in the mathematical literature before the eighteenth century. The vinculum was used extensively, usually as an overline, but Chuquet in 1484 used the underline version.
The vinculum is used as part of the notation of a radical to indicate the radicand whose root is being indicated. In the following, the quantity is the whole radicand, and thus has a vinculum over it:
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