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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together, especially in written mathematics, but in modern mathematics its use for this purpose has almost entirely been replaced by the use of
570:
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722:. 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
50:
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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).
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Formerly its main use was as a notation to indicate a group (a bracketing device serving the same function as parentheses):
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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.
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was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today.
314:
whose values are multiplied by 1,000. Today, however, the common usage of a vinculum to indicate the repetend of a
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218:
286:
128:
84:
331:
784:
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579:, a vinculum may be used to represent the operation of inversion (also known as the NOT function):
334:(who had himself not used this notation). However, earlier versions, such as using an underline as
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327:
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1106:
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Conférence
Intercantonale de l'Instruction Publique de la Suisse Romande et du Tessin (2011).
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968:. Translated by David Bellos, E. F. Harding, Sophie MENGNIU, Ian Monk. John Wiley & Sons.
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is necessary to override the math-mode (here invoked by the dollar signs) which the
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The
Universal History of Numbers: From Prehistory to the Invention of the Computer
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Logarithm of a number less than 1 can conveniently be represented using vinculum:
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565:{\displaystyle \log 2=0.301\Rightarrow \log 0.2={\overline {1}}.301=-0.699}
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did in 1637, using it only in relation to the radical sign, were common.
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In India, the use of this notation is still tested in primary school.
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Vulgar and decimal fractions (The Mount Vernon
Arithmetic Part II)
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is a significant exception and reflects the original usage.
285: 'fetter, chain, tie') is a horizontal line used in
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is the whole radicand, and thus has a vinculum over it:
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Similarly, it is used to show the repeating terms in a
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is being indicated. In the following, the quantity
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The vinculum, in its general use, was introduced by
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737:The vinculum is used as part of the notation of a
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248:
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155:
111:
44:
707:, which would be written more commonly today as
1006:. Mathématiques 9-10-11. LEP. pp. 20–21.
289:for various purposes. It may be placed as an
16:Horizontal line used in mathematical notation
8:
910:in word processing and text editing software
880:, a text <text> can be overlined with
408:A vinculum can indicate the repetend of a
1042:"BODMAS (Basic) (Practice) | Week 1"
983:A Concrete Introduction to Higher Algebra
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703:first and then subtract the result from
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490:{\displaystyle {\overline {2+3i}}=2-3i}
398:{\displaystyle {\overline {\rm {AB}}}.}
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637:are the only numbers that have these.
45:{\displaystyle {\overline {\rm {AB}}}}
7:
726:in 1484 used the underline version.
685:{\displaystyle a-{\overline {b+c}},}
987:(3rd ed.). Springer. pp.
936:A History of Mathematical Notations
616:{\displaystyle Y={\overline {AB}},}
338:did in 1484, or in limited form as
330:in 1646 as he edited the works of
249:{\displaystyle a-{\overline {b+c}}}
882:$ \overline{\mbox{<text>}}$
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156:{\displaystyle Y={\overline {AB}}}
112:{\displaystyle {\overline {a+bi}}}
33:
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902:Overline § Math and science
908:Overline § Implementations
844:Overline § Implementations
939:. Vol. I. Dover. p.
817:{\displaystyle {\sqrt{ab+2}}.}
525:
1:
1091:"Periodic Continued Fraction"
202:{\displaystyle {\sqrt{ab+2}}}
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635:Quadratic irrational numbers
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433:A vinculum can indicate the
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37:
979:Childs, Lindsay N. (2009).
631:periodic continued fraction
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429:= 0.1428571428571428571...
355:A vinculum can indicate a
166:boolean NOT (A AND B)
933:Cajori, Florian (2012) .
77:0.1428571428571428571...
55:line segment from A to B
1067:Abbott, Jacob (1847) ,
964:Ifrah, Georges (2000).
904:similar-looking symbols
303:mathematical expression
1139:Elementary mathematics
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733:As a part of a radical
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1134:Mathematical symbols
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771:{\displaystyle ab+2}
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367:are the endpoints:
312:mark Roman numerals
260:bracketing function
1107:Weisstein, Eric W.
1088:Weisstein, Eric W.
1031:, pp. 390–391
866:COMBINING OVERLINE
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256:= a − (b + c)
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1071:, p. 27
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1004:Aide-mémoire
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884:. The inner
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1055:Cajori 2012
1029:Cajori 2012
1017:Cajori 2012
890:\overline{}
308:parentheses
1128:Categories
1110:"Vinculum"
920:References
849:In Unicode
641:Historical
273:(from
1115:MathWorld
1096:MathWorld
914:Underline
892:demands.
838:Encodings
829:Descartes
675:¯
659:−
606:¯
557:−
546:¯
532:
526:⇒
514:
479:−
468:¯
388:¯
340:Descartes
298:underline
242:¯
226:−
149:¯
105:¯
75:repeated
38:¯
896:See also
862:◌̅
827:In 1637
743:radicand
292:overline
281:vinculum
271:vinculum
886:\mbox{}
739:radical
724:Chuquet
420:⁄
412:value:
336:Chuquet
322:History
63:⁄
947:
858:
856:U+0305
745:whose
427:142857
359:where
351:Modern
70:142857
991:-188.
878:LaTeX
560:0.699
523:0.301
437:of a
346:Usage
277:
275:Latin
945:ISBN
747:root
699:and
551:.301
425:= 0.
363:and
68:= 0.
989:183
941:384
876:In
872:TeX
712:− (
575:In
535:0.2
529:log
511:log
295:or
1130::
1112:.
1093:.
943:.
716:+
633:.
441::
269:A
1118:.
1099:.
1044:.
953:.
812:.
806:n
801:2
798:+
795:b
792:a
766:2
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757:a
720:)
718:c
714:b
710:a
705:a
701:c
697:b
680:,
671:c
668:+
665:b
656:a
611:,
602:B
599:A
593:=
590:Y
554:=
543:1
538:=
520:=
517:2
485:i
482:3
476:2
473:=
464:i
461:3
458:+
455:2
422:7
418:1
393:.
384:B
381:A
365:B
361:A
238:c
235:+
232:b
223:a
194:n
189:2
186:+
183:b
180:a
145:B
142:A
136:=
133:Y
101:i
98:b
95:+
92:a
65:7
61:1
34:B
31:A
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