Vinculum (symbol)

A vinculum can indicate a line segment where A and B are the endpoints:

• ${\displaystyle {\overline {\rm {AB}}}.}$

A vinculum can indicate the repetend of a repeating decimal value:

• ​¹⁄₇ = 0.142857 = 0.1428571428571428571...

In Boolean logic, a vinculum may be used to represent the operation of inversion (also known as the NOT function):

• ${\displaystyle Y={\overline {\rm {AB}}},}$

meaning that Y is false only when both A and B are both true - or by extension, Y is true when either A or B is false.

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):

${\displaystyle a-{\overline {b+c}},}$

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.[4]

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 ${\displaystyle ab+2}$ is the whole radicand, and thus has a vinculum over it:

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

In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today.[5]

The symbol used to indicate a vinculum need not be a line segment (overline or underline); sometimes braces can be used (pointing either up or down).[6]

• Overline § Math and science similar-looking symbols
• Overline § Implementations in word processing and text editing software
• Underline

• Weisstein, Eric W. "Periodic Continued Fraction". MathWorld.
• Weisstein, Eric W. "Vinculum". MathWorld.