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    A vinculum (from Latin vinculum 'fetter, chain, tie') is a horizontal line used in mathematical notation for various purposes. It may be placed as an overline or underline above or below a mathematical expression to group the expression's elements. Historically, vincula were extensively used to group items together, especially in written mathematics, but in modern mathematics its use for this purpose has almost entirely been replaced by the use of parentheses. It was also used to mark Roman numerals whose values are multiplied by 1,000. Today, however, the common usage of a vinculum to indicate the repetend of a repeating decimal is a significant exception and reflects the original usage.


    History


    The vinculum, in its general use, was introduced by Frans van Schooten in 1646 as he edited the works of François Viète (who had himself not used this notation). However, earlier versions, such as using an underline as Chuquet did in 1484, or in limited form as Descartes did in 1637, using it only in relation to the radical sign, were common.


    Usage




    = Modern

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







    A
    B

    ¯


    .


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


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

    1⁄7 = 0.142857 = 0.1428571428571428571...
    A vinculum can indicate the complex conjugate of a complex number:







    2
    +
    3
    i

    ¯


    =
    2
    −
    3
    i


    {\displaystyle {\overline {2+3i}}=2-3i}


    Logarithm of a number less than 1 can conveniently be represented using vinculum:




    log
    ⁡
    2
    =
    0.301
    ⇒
    log
    ⁡
    0.2
    =


    1
    ¯


    .301
    =
    −
    0.699


    {\displaystyle \log 2=0.301\Rightarrow \log 0.2={\overline {1}}.301=-0.699}


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




    Y
    =



    A
    B

    ¯


    ,


    {\displaystyle Y={\overline {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.


    = Historical

    =
    Formerly its main use was as a notation to indicate a group (a bracketing device serving the same function as parentheses):




    a
    −



    b
    +
    c

    ¯


    ,


    {\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.
    In India, the use of this notation is still tested in primary school.


    = As a part of a radical

    =
    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



    a
    b
    +
    2


    {\displaystyle ab+2}

    is the whole radicand, and thus has a vinculum over it:







    a
    b
    +
    2


    n



    .


    {\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.
    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).


    Encodings




    = Unicode

    =
    U+0305 ◌̅ COMBINING OVERLINE


    = TeX

    =
    In LaTeX, a text can be overlined with $\overline{\mbox{}}$. The inner \mbox{} is necessary to
    override the math-mode (here invoked by the dollar signs) which the \overline{} demands.


    See also


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


    References




    External links


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

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Vinculum Symbol

Vinculum Symbol

vinculum logo transparent - Saskatchewan Mathematics Teachers

vinculum logo transparent - Saskatchewan Mathematics Teachers' Society

Vinculum Definition (Illustrated Mathematics Dictionary)

Vinculum Definition (Illustrated Mathematics Dictionary)

Vinculum Definition (Illustrated Mathematics Dictionary)

Vinculum Definition (Illustrated Mathematics Dictionary)

Vinculum -- from Wolfram MathWorld

Vinculum -- from Wolfram MathWorld

Vinculum -- from Wolfram MathWorld

Vinculum -- from Wolfram MathWorld

Vinculum -- from Wolfram MathWorld

Vinculum -- from Wolfram MathWorld

Vinculum Symbol Microsoft Word

Vinculum Symbol Microsoft Word

Stream vinculum music | Listen to songs, albums, playlists for free on ...

Stream vinculum music | Listen to songs, albums, playlists for free on ...

Vinculum Overview

Vinculum Overview

Vinculum

Vinculum

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vinculum symbol

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Vinculum In Math: Definition And Examples – Math Mum

Apr 29, 2023 · A vinculum is a horizontal line that groups together expressions in mathematics. Learn how to use it in fractions, radicals, complex numbers, and repeating decimals with …

Vinculum|Definition & Meaning - The Story of Mathematics

Learn what a vinculum is and how it is used in mathematics. A vinculum is a horizontal line that groups expressions, indicates fractions, or shows recurring d…

Vinculum -- from Wolfram MathWorld

4 days ago · Weisstein, Eric W. "Vinculum." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Vinculum.html. A horizontal line placed above multiple …

Vinculum Definition (Illustrated Mathematics Dictionary) - Math is …

A vinculum is a horizontal line that groups expressions or fractions. Learn how to use it in math symbols and notation with examples and diagrams.

Vinculum (symbol) - Simple English Wikipedia, the free encyclopedia

A vinculum is a horizontal line over a mathematical expression that shows it belongs together as a group. Learn how to use vinculum for repeating digits, fractions, and radicals with examples …

Bar -- from Wolfram MathWorld

4 days ago · If the bar is placed over a single symbol, as in x^_ (voiced "x-bar"), it is sometimes called a macron. If placed over multiple symbols (especially in the context of a radical), it is known as a vinculum.

Go Figure!: Do You Know What a Vinculum Is? Here's …

Aug 29, 2024 · The line of a radical sign or the long division house is also called a vinculum. The symbol is utilized to separate the dividend from the divisor, and is drawn as a right parenthesis with an attached vinculum (see illustration above) …

Symbols:Brackets/Vinculum - ProofWiki

Sep 4, 2024 · Symbol. A vinculum is a line drawn over terms in parenthesis: $\overline {a + b}$ The $\LaTeX$ code for \(\overline {a + b}\) is \overline {a + b}. Examples Square Root. …

Vinculum (symbol) - Wikiwand

A vinculum is a horizontal line put over a mathematical expression. It shows that it belongs together as a group. (Vinculum is Latin for "chain".) Examples are: 1. groups of digits repeating …