Degree sign

°

The degree symbol (°) is used as a symbol for the first divisor of a scale. If necessary, characters are available for the first ( minute , ′), second ( second , ″) and third ( tertie , ′ ′ ′) divider of this divider. In general, these characters are attached directly to the numerical value; however, one or more letters follow to indicate the scale used - as is the case with temperatures, for example - a (narrow) space is placed between the number and the unit.

use

Today the symbols are mainly used for angles (78 ° 56 ′ 34.12 ″ in degrees, minutes and seconds [-fractions]) and the position information derived therefrom (51 ° north latitude). Historically, and in remnants still today, it is also used with length measures , especially in the factor twelve series rod (°), foot (′), inch (″) and line (′ ′ ′), in some cases also a point (′ ′ ′ ′), As well as with time units in the factor sixty series hour (°), minute (′) and second (″), earlier sometimes additionally tertie (′ ′ ′) and fourth (′ ′ ′ '); very rare, first with Roger Bacon 1267 as Latin quarta ). In the publishing industry and in libraries it has long been used to identify the book format , with some libraries switching to specifying new entries in centimeters .

The degree symbol is an inseparable part (and without a space to the letter but always with a (narrow) space to the numerical value) of the symbols of temperature units, such as degrees Celsius (° C), degrees Fahrenheit (° F), degrees delisle (° De), degrees Réaumur (° Ré), degrees Rømer (° Rø), degrees Newton (° N) and degrees Rankine (° Ra), but not for the unit Kelvin (K). There are no further divisors for any of these scales.

In MS Word , the character is used as a symbol for non-breaking spaces . (Only visible on the screen if 'Show control characters' is activated.)

history

The first known written evidence for the modern use of the degree symbol in mathematics dates back to 1569, where the use clearly shows that the symbol represents a small superscript zero, corresponding to the stroke notation of the sexagesimal subdivisions of the degree , such as minute ′ , second ″ and Tertie ‴, derived from small superscript Roman numerals .

An alternative theory of the origin of the degree sign states that it comes from an Egyptian hieroglyph , which represents the sun and means day .

Representation in computer systems and replacement

Coding

In the international character coding system Unicode , the characters are in these positions:

°	U + 00B0	DEGREE SIGN (degree sign)
′	U + 2032	PRIME (minute sign)
″	U + 2033	DOUBLE PRIME (second)
‴	U + 2034	TRIPLE PRIME (Tertie)

None of the characters is in ASCII - character set included, which is why many older computer systems they could not represent. ISO 6937 and the widely used ISO 8859-1 (aka Latin-1) and other parts of the ISO-8859 family contain the degree symbol. Minute and second are approximated in both ASCII and ISO 8859 by '(U + 0027) or "(U + 0022), so they share their representation with the apostrophe and most of the quotation marks .

In the Internet document format HTML , the characters can be encoded as follows:

	Hexadecimal	Decimal	Named
°	`°`	`°`	`°`
′	`′`	`′`	`′`
″	`″`	`″`	`″`
‴	`‴`	`‴`

The special Unicode characters ℃ ( U+2103) and ℉ ( U+2109) exist for temperature specifications in degrees Celsius and degrees Fahrenheit, but the Unicode Consortium advises against using them.

keyboard

On the German keyboard , the degree symbol is on the top left key above the circumflex accent (^) (to be pressed together with the shift key).

With the standard keyboard layout T2 according to the revised German standard DIN 2137-1 : 2012-06, the subdivision character ′ is entered for minute with Alt Gr+ f, and the character ″ for second with Alt Gr+ g.

On German keyboards according to previous versions of the standard (or assignment T1 according to the new standard), 'and "can be used as replacement characters. These are located above the pound sign (next to the enter key ) or above the number 2. Both require you to hold down the for input Shift key.

On the German-Swiss keyboard , the ° symbol is the second assignment on the key with the paragraph symbol (to the left of the number 1).

With the Neo keyboard layout , the degree symbol is on Shift + 1.

Although the degree symbol is quite common, a corresponding key is missing on both the English and American keyboards, except in their less common international variants. The entry must therefore be made via a character table or under Windows via Alt+ 0176.

The Compose key can be used to generate the degree symbol under Unix systems, including Linux (Compose key followed by o, o).

Replacement and Similar Characters

If the character cannot be displayed because it is missing in the font or character set used , it should be replaced by the appropriate word, in German "Grad".

Today, however, replacement is hardly necessary for technical reasons. Even if the keyboard used does not have the character, it can practically always be inserted using a corresponding function in the language, the operating system or the text editor .

The OMS coding used by TeX for mathematical characters only knows the circle operator . The degree symbol is generated by superscript ( ). ${\ displaystyle \ circ}$ ${\ displaystyle ^ {\ circ}}$ ^\circ

Similar looking characters are:

º (U + 00BA masculine ordinal indicator , masculine ordinal sign Ordinal-o, underlined in some fonts)
˚ (U + 02DA ring above , free-standing Kroužek , free-standing circle / ring accent)
ᵒ (U + 1D52 modifier letter small o , superscript small letter o)
ᴼ (U + 1D3C modifier letter capital o , superscript capital letter O)
⁰ (U + 2070 superscript zero , superscript zero)

Individual evidence

↑ Useful key combination: Protected spaces in Word documents - Digital - Augsburger Allgemeine. In: augsburger-allgemeine.de. Retrieved May 23, 2017 .
^ Cajori, Florian: A History of Mathematical Notations . Dover Publications, New York 1993, ISBN 0-486-67766-4 (unmodified reprint of 1st edition 1928-1929).
↑ Unicode Consortium: The Unicode Standard, Version 5.0. (pdf) 2007, accessed on December 28, 2016 (English).

[1] Useful key combination: Protected spaces in Word documents - Digital - Augsburger Allgemeine. In: augsburger-allgemeine.de. Retrieved May 23, 2017 .

[2] Cajori, Florian: A History of Mathematical Notations . Dover Publications, New York 1993, ISBN 0-486-67766-4 (unmodified reprint of 1st edition 1928-1929).

[3] Unicode Consortium: The Unicode Standard, Version 5.0. (pdf) 2007, accessed on December 28, 2016 (English).