Root sign

√
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	¬

The root sign (√) is the symbol used in mathematical notation for the square root of a number or for the square root . By specifying a root exponent, roots with any exponent, such as cube roots , are noted with the help of the root symbol .

history

The root sign √ probably comes from the small letter r and stands for square root. An alternative origin is a point with a decorative spread, comparable to a quarter note. It was first used in 1525 by the German mathematician Christoph Rudolff . The extension of the r over the full term - the Vinculum - was introduced in 1637 in the book Discours de la méthode by Descartes . The hieroglyph for the square root in ancient Egypt is a right angle. This notation is used in the Lahunpapyri .

Traditions of the formula set

The different traditions of the formula set reveal the above-mentioned origin more or less clearly. The shape of the root symbol in the American formula shows little resemblance to the small r . In particular, the oblique downward stroke on the left side of the character distinguishes it from the form in other traditions of the formula set. Depending on its size, the root sign shows slightly different variants, as can be seen in the following formula:

{\ displaystyle {\ sqrt {\ sqrt [{n}] {\ sqrt [{3}] {3}}}} \ ;.}

The root sign in the German and Russian formula sets, however, always shows the same shape regardless of size. The German form of the root sign is very similar to the lowercase letter r . However, the stroke on the left does not necessarily have the same height as the stroke above the radicand, as shown in the picture German form of the root sign , so that the transition to the Russian form is fluid. The root sign in the Russian set of formulas shows a form that has properties of both the German and the American form.

German form of the root symbol, typically used in DIN standards

Russian form of the root sign

Root set by TeX

Web typographic representation

Problems with this special character arise in the electronic representation, because it can usually not be entered directly via the keyboard. If the root symbol is entered as a character in Unicode or HTML , the problem arises that the radicand is not "below" the root because the letter set does not allow the root character to be extended in a meaningful way.

Coding in Unicode, HTML and LaTeX
character	Unicode		designation	HTML			Latex
character	position	designation	designation	hexadecimal	decimal	named	Latex
√	`U+221A`	square root	square root	& # x221a;	& # 8730;	?	`\sqrt`
∛	`U+221B`	cube root	Cube root	& # x221b;	& # 8731;		`\sqrt[3]`
∜	`U+221C`	fourth root	Fourth root	& # x221c;	& # 8732;		`\sqrt[4]`

literature

Ulrich Felgner: About the origin of the root sign. In: Mathematical semester reports. Vol. 52, No. 1, 2005, Springer, pp. 1–7, ISSN 0720-728X ( doi : 10.1007 / s00591-004-0083-4 )
Florian Cajori: A History of Mathematical Notations (Two Volume in One) , Cosimo, 2011 (reprint). ISBN 1616405716 .

Web links

Wiktionary: Root signs - explanations of meanings, word origins, synonyms, translations

Individual evidence

^ Cajori, p. 375.
↑ According to information from DIN, Standards Committee Technical Basics, in Aug. 2010, details are not specified. This representation is a combination of many similar representations in the standards.
↑ Valentin Zaitsev, Andrew Janishewsky, Alexander Berdnikov: Russian Typographical Traditions in Mathematical Literature . In: EuroTeX'99 proceedings. ( Memento of September 28, 2012 in the Internet Archive ) (PDF 196 kB, English).

[1] Cajori, p. 375.

[2] According to information from DIN, Standards Committee Technical Basics, in Aug. 2010, details are not specified. This representation is a combination of many similar representations in the standards.

[3] Valentin Zaitsev, Andrew Janishewsky, Alexander Berdnikov: Russian Typographical Traditions in Mathematical Literature . In: EuroTeX'99 proceedings. ( Memento of September 28, 2012 in the Internet Archive ) (PDF 196 kB, English).