Division sign: Difference between revisions
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The '''division sign''' ({{char|'''÷'''}}) is a [[Glossary of mathematical symbols|mathematical symbol]] consisting of a short horizontal line with a dot above and another dot below, used in [[Anglophone]] countries to indicate the operation of [[Division (mathematics)|division]]. This usage is not universal and the symbol has different meanings in other countries. Consequently, its use to denote division is | The '''division sign''' ({{char|'''÷'''}}) is a [[Glossary of mathematical symbols|mathematical symbol]] consisting of a short horizontal line with a dot above and another dot below, used in [[Anglophone]] countries to indicate the operation of [[Division (mathematics)|division]]. This usage is not universal and the symbol has different meanings in other countries. Consequently, its use to denote division is deprecated in the [[ISO 80000-2]] standard for notations used in mathematics, science and technology.<ref name=ISO /> | ||
==In mathematics== | ==In mathematics== | ||
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{{further|Division (mathematics)#Notation}} | {{further|Division (mathematics)#Notation}} | ||
The [[obelus]], a historical [[glyph]] consisting of a horizontal line with (or without) one or more dots, was first used as a symbol for division in 1659, in the [[algebra]] book ''{{lang|de|Teutsche Algebra}}'' by [[Johann Rahn]], although previous writers had used the same symbol for subtraction.<ref name="Cajori">{{cite book |title=A history of mathematical notations |volume= 1. Notations in Elementary Mathematics |publisher=The Open Court Company |year=1928 |first=Florian |last=Cajori |author-link=Florian Cajori |pages=242, 270–271 |url=https://archive.org/details/in.ernet.dli.2015.200372/page/n261/mode/2up }} [https://archive.org/details/in.ernet.dli.2015.200372/page/n289/mode/2up pp 270,271] </ref> Some near-contemporaries believed that [[John Pell (mathematician)|John Pell]], who edited the book, may have been responsible for this use of the symbol.<ref name="Cajori" /> Other symbols for division include the [[slash (punctuation)|slash]] or solidus {{char|/}}, the [[colon (punctuation)|colon]] {{char|:}}, and the [[fraction (mathematics)#Vocabulary|fraction bar]] (the horizontal bar in a vertical fraction).<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Division|url=https://mathworld.wolfram.com/Division.html|access-date=2020-08-26|website=mathworld.wolfram.com|language=en}}</ref><ref>{{Cite web|title=Division|url=https://www.mathsisfun.com/numbers/division.html|access-date=2020-08-26|website=www.mathsisfun.com}}</ref> The ISO 80000-2 standard for mathematical notation recommends only the solidus {{char|/}} or "fraction bar" for division, or the "colon" {{char|:}} for [[ratio]]s; it says that the {{char|÷}} sign "should not be used" for division.<ref name=ISO>ISO 80000-2, Section 9 "Operations", 2-9.6</ref> | The [[obelus]], a historical [[glyph]] consisting of a horizontal line with (or without) one or more dots, was first used as a symbol for division in 1659, in the [[algebra]] book ''{{lang|de|Teutsche Algebra}}'' by [[Johann Rahn]], although previous writers had used the same symbol for subtraction.<ref name="Cajori">{{cite book |title=A history of mathematical notations |volume= 1. Notations in Elementary Mathematics |publisher=The Open Court Company |year=1928 |first=Florian |last=Cajori |author-link=Florian Cajori |pages=242, 270–271 |url=https://archive.org/details/in.ernet.dli.2015.200372/page/n261/mode/2up }} [https://archive.org/details/in.ernet.dli.2015.200372/page/n289/mode/2up pp 270,271] </ref> Some near-contemporaries believed that [[John Pell (mathematician)|John Pell]], who edited the book, may have been responsible for this use of the symbol.<ref name="Cajori" /> Other symbols for division include the [[slash (punctuation)|slash]] or solidus {{char|/}}, the [[colon (punctuation)|colon]] {{char|:}}, and the [[fraction (mathematics)#Vocabulary|fraction bar]] (the horizontal bar in a vertical fraction).<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Division|url=https://mathworld.wolfram.com/Division.html|access-date=2020-08-26|website=mathworld.wolfram.com|language=en}}</ref><ref>{{Cite web|title=Division|url=https://www.mathsisfun.com/numbers/division.html|access-date=2020-08-26|website=www.mathsisfun.com}}</ref> The ISO 80000-2 standard for mathematical notation in science and technology recommends only the solidus {{char|/}} or "fraction bar" for division, or the "colon" {{char|:}} for [[ratio]]s; it says that the {{char|÷}} sign "should not be used" for division.<ref name=ISO>BS ISO 80000-2, "Quantities and units Part 2: Mathematical signs and symbols to be used in the natural sciences and technology", Section 9 "Operations", 2-9.6</ref> | ||
In [[Italy]], [[Poland]] and [[Russia]], the {{char|÷}} sign was sometimes used to denote a [[Interval (mathematics)|range of values]], and in [[Scandinavia]]n countries it was, and sometimes still is, used as a negation sign:<ref>{{cite book |chapter-url=https://www.unicode.org/versions/Unicode10.0.0/ch06.pdf#G7935 | page=280, Obelus | chapter = 6. Writing Systems and Punctuation | publisher= Unicode Consortium | title = The Unicode® Standard: Version 10.0 – Core Specification | date= June 2017}}</ref> the [[Unicode Consortium]] has allocated a separate [[code point]], {{unichar|2052|commercial minus sign|nlink=}} for this usage uniquely;<ref name=Silli1>{{cite web |title=Too narrowly defined: DIVISION SIGN & COLON |url=http://www.unicode.org/mail-arch/unicode-ml/y2012-m07/0053.html | author = Leif Halvard Silli | website= Unicode.org}}</ref><ref name=Silli2>{{cite web |url=https://www.unicode.org/mail-arch/unicode-ml/y2014-m01/0018.html | title= Commercial minus as italic variant of division sign in German and Scandinavian context | author = Leif Halvard Silli | website= Unicode.org}}</ref> the exact form of the symbol displayed is typeface (font) dependent. | In [[Italy]], [[Poland]] and [[Russia]], the {{char|÷}} sign was sometimes used to denote a [[Interval (mathematics)|range of values]], and in [[Scandinavia]]n countries it was, and sometimes still is, used as a negation sign:<ref>{{cite book |chapter-url=https://www.unicode.org/versions/Unicode10.0.0/ch06.pdf#G7935 | page=280, Obelus | chapter = 6. Writing Systems and Punctuation | publisher= Unicode Consortium | title = The Unicode® Standard: Version 10.0 – Core Specification | date= June 2017}}</ref> the [[Unicode Consortium]] has allocated a separate [[code point]], {{unichar|2052|commercial minus sign|nlink=}} for this usage uniquely;<ref name=Silli1>{{cite web |title=Too narrowly defined: DIVISION SIGN & COLON |url=http://www.unicode.org/mail-arch/unicode-ml/y2012-m07/0053.html | author = Leif Halvard Silli | website= Unicode.org}}</ref><ref name=Silli2>{{cite web |url=https://www.unicode.org/mail-arch/unicode-ml/y2014-m01/0018.html | title= Commercial minus as italic variant of division sign in German and Scandinavian context | author = Leif Halvard Silli | website= Unicode.org}}</ref> the exact form of the symbol displayed is typeface (font) dependent. | ||
Latest revision as of 18:50, 17 June 2025
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The division sign (Template:Char) is a mathematical symbol consisting of a short horizontal line with a dot above and another dot below, used in Anglophone countries to indicate the operation of division. This usage is not universal and the symbol has different meanings in other countries. Consequently, its use to denote division is deprecated in the ISO 80000-2 standard for notations used in mathematics, science and technology.[1]
In mathematics
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The obelus, a historical glyph consisting of a horizontal line with (or without) one or more dots, was first used as a symbol for division in 1659, in the algebra book Script error: No such module "Lang". by Johann Rahn, although previous writers had used the same symbol for subtraction.[2] Some near-contemporaries believed that John Pell, who edited the book, may have been responsible for this use of the symbol.[2] Other symbols for division include the slash or solidus Template:Char, the colon Template:Char, and the fraction bar (the horizontal bar in a vertical fraction).[3][4] The ISO 80000-2 standard for mathematical notation in science and technology recommends only the solidus Template:Char or "fraction bar" for division, or the "colon" Template:Char for ratios; it says that the Template:Char sign "should not be used" for division.[1]
In Italy, Poland and Russia, the Template:Char sign was sometimes used to denote a range of values, and in Scandinavian countries it was, and sometimes still is, used as a negation sign:[5] the Unicode Consortium has allocated a separate code point, Template:Unichar for this usage uniquely;[6][7] the exact form of the symbol displayed is typeface (font) dependent.
In computer systems
Encoding
The symbol was assigned to code point 0xF7 in ISO 8859-1, as the "division sign". This encoding was transferred to Unicode as U+00F7.[8] In HTML, it can be encoded as ÷ or ÷ (at HTML level 3.2), or as ÷.
Unicode provides various division symbols:[9]
| Codepoint | Name | Symbol |
|---|---|---|
| U+00F7 | Division Sign | ÷ |
| U+27CC | Long Division | ⟌ |
| U+2215 | Division Slash | ∕ |
| U+2A38 | Circled Division Sign | ⨸ |
| U+2797 | Heavy Division Sign | ➗ |
| U+2298 | Circled Division Slash | ⊘ |
| U+22C7 | Division Times | ⋇ |
| U+29BC | Circled Anticlockwise-Rotated Division Sign | ⦼ |
See also
Notes
External links
- Jeff Miller: Earliest Uses of Various Mathematical Symbols
- Michael Quinion: Where our arithmetic symbols come from
- ↑ a b BS ISO 80000-2, "Quantities and units Part 2: Mathematical signs and symbols to be used in the natural sciences and technology", Section 9 "Operations", 2-9.6
- ↑ a b Script error: No such module "citation/CS1". pp 270,271
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