Prime (symbol)


The prime symbol, double prime symbol, triple prime symbol, and quadruple prime symbol are used to designate units and for other purposes in mathematics, the sciences, linguistics and music.
Although the characters differ little in appearance from those of the apostrophe or the single or double quotation mark, the appropriate uses of the prime symbol are different. However, an apostrophe is often used in place of the prime, due to the lack of the prime and double prime symbols either on keyboards. These substitutions would not normally be considered appropriate in formal materials or in typesetting.
The prime symbol is not related to prime numbers.

Designation of units

The prime symbol is commonly used to represent feet, and the double prime is used to represent inches. The triple prime as used in watchmaking represents a ligne.
Primes are also used for angles. The prime symbol is used for arcminutes, the double prime for arcseconds. As an angular measurement, means 3 degrees, 5 arcminutes and 30 arcseconds. In historical astronomical works the triple prime was used to denote "thirds" and a quadruple prime denotes "fourths" but modern usage has replaced this with decimal values of arcseconds.
Primes are sometimes used to indicate minutes and double primes to indicate seconds of time, as in the John Cage composition 4'33", pronounced 4 minutes 33 seconds. This notation only applies to duration, and is seldom used for durations longer than 60 minutes.

Use in mathematics, statistics, and science

In mathematics, the prime is generally used to generate more variable names for things which are similar, without resorting to subscripts – generally means something related to or derived from. For example, if a point is represented by the Cartesian coordinates, then that point rotated, translated or reflected might be represented as.
Usually, the meaning of is defined when it is first used, but sometimes its meaning is assumed to be understood:
The prime is said to "decorate" the letter to which it applies. The same convention is adopted in functional programming, particularly in Haskell.
In geometry, geography and astronomy, prime and double prime are used as abbreviations for minute and second of arc.
In physics, the prime is used to denote variables after an event. For example, would indicate the velocity of object A after an event. It is also commonly used in relativity: the event at in frame, has coordinates in frame.
In chemistry, it is used to distinguish between different functional groups connected to an atom in a molecule, such as and, representing different alkyl groups in an organic compound. The carbonyl carbon in proteins is denoted as, which distinguishes it from the other backbone carbon, the alpha carbon, which is denoted as. In physical chemistry, it is used to distinguish between the lower state and the upper state of a quantum number during a transition. For example, denotes the upper state of the quantum number while denotes the lower state of the quantum number.
In molecular biology, the prime is used to denote the positions of carbon on a ring of deoxyribose or ribose. The prime distinguishes places on these two chemicals, rather than places on other parts of DNA or RNA, like phosphate groups or nucleic acids. Thus, when indicating the direction of movement of an enzyme along a string of DNA, biologists will say that it moves from the end to the end, because these carbons are on the ends of the DNA molecule. The chemistry of this reaction demands that the is extended by DNA synthesis. Prime can also be used to indicate which position a molecule has attached to, such as

Use in linguistics

The prime can be used in the transliteration of some languages, such as Slavic languages, to denote palatalization. Prime and double prime are used to transliterate Cyrillic yeri and yer. However, in ISO 9, the corresponding modifier letters are used instead.
Originally, X-bar theory used a bar over syntactic units to indicate bar-levels in syntactic structure, generally rendered as an overbar. While easy to write, the bar notation proved difficult to typeset, leading to the adoption of the prime symbol to indicate a bar. With contemporary development of typesetting software such as LaTeX, typesetting bars is considerably simpler; nevertheless, both prime and bar markups are accepted usages.
Some X-bar notations use a double-prime to indicate a phrasal level, indicated in most notations by "XP".

Use in music

The prime symbol is used in combination with lower case letters in the Helmholtz pitch notation system to distinguish notes in different octaves from middle C upwards. Thus represents the below middle C, represents middle C, represents the in the octave above middle C, and the in the octave two octaves above middle C. A combination of upper case letters and sub-prime symbols is used to represent notes in lower octaves. Thus represents the below the bass stave, while represents the in the octave below that.
In some musical scores, the double prime is used to indicate a length of time in seconds. It is used over a fermata denoting a long note or rest.

History

The name "prime" is something of a metonymy. Through the early part of the 20th century, the notation was read as "x prime" not because it was an x followed by a "prime symbol", but because it was the first in the series that continued with and x‴. It was only later, in the 1950s and 1960s, that the term "prime" began to be applied to the apostrophe-like symbol itself. Although it is now more common to pronounce x″ and x‴ as "x double prime" and "x triple prime", these are still sometimes pronounced in the old manner as "x second" and "x third".

Computer encodings

Unicode and HTML representations of the prime and related symbols are as follows.
The "modifier letter prime" and "modifier letter double prime" characters are intended for linguistic purposes, such as the indication of stress or the transliteration of certain Cyrillic characters.
In a context when the character set used does not include the prime or double prime character, they are often respectively approximated by ASCII apostrophe or quotation mark.
LaTeX provides an oversized prime symbol, , which, when used in super- or sub-scripts, renders appropriately; e.g., f_\prime^\prime appears as. An apostrophe,, is a shortcut for a superscript prime; e.g., appears as.