Divided sign

÷ is a redirect to this article. For further meanings see ÷ (disambiguation) .

: ÷ /
Mathematical signs
arithmetic
Plus sign	+
Minus sign	- , ./.
Mark	⋅ , ×
Divided sign	: , ÷ , /
Plus minus sign	± , ∓
Comparison sign	< , ≤ , = , ≥ , >
Root sign	√
Percent sign	%
Analysis
Sum symbol	Σ
Product mark	Π
Difference sign , Nabla	∆ , ∇
Prime	′
Partial differential	∂
Integral sign	∫
Concatenation characters	∘
Infinity symbol	∞
geometry
Angle sign	∠ , ∡ , ∢ , ∟
Vertical , parallel	⊥ , ∥
Triangle , square	△ , □
Diameter sign	⌀
Set theory
Union , cut	∪ , ∩
Difference , complement	∖ , ∁
Element character	∈
Subset , superset	⊂ , ⊆ , ⊇ , ⊃
Empty set	∅
logic
Follow arrow	⇒ , ⇔ , ⇐
Universal quantifier	∀
Existential quantifier	∃
Conjunction , disjunction	∧ , ∨
Negation sign	¬

Divided characters , division characters or division characters are special characters that are regularly used to represent the mathematical operator for division .

Division symbols

A colon (:), a colon with a middle bar (÷) or a slash (/) are used as dividing characters in the text . Fractions are represented by a fraction line that is similar to the forward slash in the text. In the formula set, the numerator and denominator of a fraction are displayed one above the other, with the now horizontal fraction line as the dividing line.

In most countries, including Germany, the colon (:) is preferred in school mathematics; In the English-speaking world and on pocket calculators , the Obelus symbol (÷) is usually used. In higher mathematics, the fractional spelling ( and rarely ) or the spelling as multiplication with the reciprocal value ( ) can be found almost exclusively, which provides the necessary clarity, especially with non-commutative multiplication. The slash (/) is found mainly in programming languages. ${\displaystyle {\tfrac {a}{b}}}$ ${\displaystyle {}^{a}/_{b}}$ ${\displaystyle ab^{-1}}$

Note the different associativity of the operators , if applicable .

History of symbols

The oldest symbol appears to be the forward slash (/). It was first used by the English mathematician William Oughtred in his work Clavis Mathematicae, published in London in 1631.

The German scientist Gottfried Wilhelm Leibniz used the colon (:). Leibniz first used the division colon in 1684 in Acta Eruditorum . Before Leibniz, the Englishman Johnson published the symbol in a book in 1633, but only as a fraction symbol and not for the division in the narrower sense.

Johann Rahn introduced the symbol (÷) composed of a colon and a dash for division . Together with the symbol for multiplication (∗), this appears for the first time in his book Teutsche Algebra, published in 1659. Rahn's split sign is sometimes referred to as the English split sign because it is more common in the English-speaking world. However, its origin lies in Germany.

Leonardo Fibonacci was the first European mathematician to use the horizontal fraction line derived from Islamic mathematics .

Representation in computer systems

Coding

The international character encoding standard Unicode contains several divided characters and characters for closely related applications. They are in the following positions:

Coding in Unicode, HTML and LaTeX

character	Unicode		designation	HTML			Latex
	position	designation		hexadecimal	decimal	named
:	U + 003A	colon	Colon	& # x003A;	& # 58;		:
÷	U + 00F7	division sign	Divided sign	& # x00F7;	& # 247;	& divide;	\ div
∕	U + 2215	division slash	Split line	& # x2215;	& # 8725;		Note
⁄	U + 2044	fraction slash	Fraction line	& # x2044;	& # 8260;	& frasl;	Note
∶	U + 2236	ratio	(in relation to	& # x2236;	& # 8758;		\ ratio

^Note They are almost generated when using the LaTeX package xfrac .

In ASCII - character set is merely contain the colon, which is why many older computer systems could only represent him. According to Unicode, U + 2236 is to be preferred instead of the simple colon for divisions, since the simple colon also has other semantics.

The distinction between division slash and fraction slash is ultimately of a semantic nature , even if the Unicode consortium intended something different according to a technical note: “ … the 'fraction slash' U + 2044… builds up to a skewed fraction, the 'division slash' U + 2215… builds up to a potentially large linear fraction,… ”( Murray Sargent III , German:“… the 'fraction line' U + 2044… causes an oblique fraction, the 'division line' U + 2215… causes a potentially large linear fraction Fraction [ Note: ie within the line], ... “) The division slash can be found in the unicode block mathematical operators , the fraction slash in the block for general punctuation .

Replacement with other characters

Due to the lack of split characters on common keyboards , the characters are often replaced by the single colon : or the single slash / , both of which already appeared in the ASCII character set.

The ASCII extensions ISO 6937 from 1983 and ISO 8859-1 (Latin 1) from 1986 contained the divided character (÷). This can be generated by pressing Alt + 0247 on the number pad.

literature

• Florian Cajori : A History of Mathematical Notations. Dover Publications, New York NY 1993, ISBN 0-486-67766-4 (reprint of the original two volume work by Open Court Publishing 1928/1929).

Individual evidence

1. ↑ Andreas de Vries: The long way of the numbers. A brief history of the decimal system. Books on Demand, Norderstedt 2011, ISBN 978-3-8423-5120-2 , p. 42.
2. ↑ Scott Pakin: The Comprehensive LaTeX Symbol List. (PDF, 8.7 MB) January 19, 2017, archived from the original on September 28, 2017 ; Retrieved on September 28, 2017 (English, linking the original results in a mirror of CTAN , the archive link compare file: Comprehensive LaTeX Symbol list.pdf ). 
3. ^ Jason C: Difference Between Unicode FRACTION SLASH and DIVISION SLASH. In: Super User. Stack Exchange, June 1, 2015, accessed November 25, 2015 . 
4. ↑ Murray Sargent III: Unicode Nearly Plain-Text Encoding of Mathematics (PDF; 1.4 MB) March 10, 2010 (English) accessed on November 25, 2015