repeated
boolean NOT (A AND B)
/math>
bracketing function
bracketing function
Vinculum usage
A vinculum () is a horizontal line used in
mathematical notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathem ...
for various purposes. It may be placed as an
overline
An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In old mathematical notation, an overline was called a '' vinculum'', a notation for grouping symbols which is expressed in m ...
(or
underline
An underscore, ; also called an underline, low line, or low dash; is a line drawn under a segment of text. In proofreading, underscoring is a convention that says "set this text in italic type", traditionally used on manuscript or typescript as ...
) over (or under) a
mathematical expression
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, f ...
to indicate that the expression is to be considered grouped together. Historically, vincula were extensively used to group items together, especially in written mathematics, but in modern mathematics this function has almost entirely been replaced by the use of
parentheses
A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. Typically deployed in symmetric pairs, an individual bracket may be identified as a 'left' or 'r ...
. 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
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational i ...
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
François Viète, Seigneur de la Bigotière ( la, Franciscus Vieta; 1540 – 23 February 1603), commonly know by his mononym, Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to i ...
(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
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between i ...
where ''A'' and ''B'' are the endpoints:
*
A vinculum can indicate the repetend of a
repeating decimal
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational i ...
value:
* = 0. = 0.1428571428571428571...
In
Boolean logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas ...
, a vinculum may be used to represent the operation of inversion (also known as the NOT function):
*
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 number In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducibl ...
s 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):
:
meaning to add ''b'' and ''c'' first and then subtract the result from ''a'', which would be written more commonly today as . 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.
As a part of a radical
The vinculum is used as part of the notation of a
radical
Radical may refer to:
Politics and ideology Politics
* Radical politics, the political intent of fundamental societal change
*Radicalism (historical), the Radical Movement that began in late 18th century Britain and spread to continental Europe an ...
to indicate the
radicand
In mathematics, a radicand, also known as an nth root, of a number ''x'' is a number ''r'' which, when raised to the power ''n'', yields ''x'':
:r^n = x,
where ''n'' is a positive integer, sometimes called the ''degree'' of the root. A root ...
whose
root
In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the su ...
is being indicated. In the following, the quantity
is the whole radicand, and thus has a vinculum over it:
:
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
In Unicode
*
TeX
In
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well.
In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms ...
, a text
can be overlined with $\overline$. The inner \mbox is necessary to
override the math-mode (here invoked by the dollar signs) which the \overline demands.
See also
* similar-looking symbols
* in word processing and text editing software
* Underline
An underscore, ; also called an underline, low line, or low dash; is a line drawn under a segment of text. In proofreading, underscoring is a convention that says "set this text in italic type", traditionally used on manuscript or typescript as ...
References
External links
*
*
{{DEFAULTSORT:Vinculum (Symbol)
Mathematical symbols
Elementary mathematics