Overline
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Description | Sample | Unicode | CSS/HTML |
---|---|---|---|
Overline (markup) |
Xx | — | text-decoration: overline;
|
Overline (character) |
‾ | U+203E | ‾ , ‾
|
X̅x̅ (combining) | U+0305 | X̅
| |
Double overline (markup) |
Xx | — | text-decoration: overline;
|
Double overline (character) |
X̿x̿ (combining) | U+033F | X̿
|
Macron (character) |
¯ | U+00AF | ¯ , ¯
|
X̄x̄ (combining) | U+0304 | X̄
| |
X̄x̄ (precomposed) | varies |
An overline, overscore, or overbar, is a
An overline, that is, a single line above a chunk of text, should not be confused with the
Uses
Medicine
In most forms of
- a, a̅, or ā for ante ("before")
- c, c̅, or c̄ for cum ("with")
- p, p̅, or p̄ for post ("after")[3]
- q, q̅, or q̄ for quisque and its inflections ("every", "each")
- s, s̅, or s̄ for sine ("without")
- x, x̅, or x̄ for exceptus and its inflections ("except")
Note, however, that abbreviations involving the letter h take their macron halfway up the ascending line rather than at the normal height for Unicode overlines and macrons:
Math and science
Decimal separator
In the
Vinculum
In mathematics, an overline can be used as a vinculum.
The vinculum can indicate a line segment:[4]The vinculum can indicate a repeating decimal value: When it is not possible to format the number so that the overline is over the digit(s) that repeat, one overline character is placed to the left of the digit(s) that repeat: Historically, the vinculum was used to group together symbols so that they could be treated as a unit. Today, parentheses are more commonly used for this purpose.
Statistics
The overline is used to indicate a
- is the average value of
Survival functions or complementary cumulative distribution functions are often denoted by placing an overline over the symbol for the cumulative: .
Negation
In set theory and some electrical engineering contexts, negation operators (also known as complement) can be written as an overline above the term or expression to be negated.[6] For example:
Common set theory notation:
Electrical engineering notation:
in which the times (cross) means multiplication, the dot means logical AND, and the plus sign means logical OR.
Both illustrate De Morgan's laws and its mnemonic, "break the line, change the sign".
Negative
In
Complex numbers
The overline notation can indicate a complex conjugate and analogous operations.[7]
- if , then
Vector
In physics, an overline sometimes indicates a
Congruence classes
Congruence modulo n is an equivalence relation, and the equivalence class of the integer a, denoted by an, is the set {... , a − 2n, a − n, a, a + n, a + 2n, ...}. This set, consisting of all the integers congruent to a modulo n, is called the congruence class, residue class, or simply residue of the integer a modulo n. When the modulus n is known from the context, that residue may also be denoted [a] or a.
Topological closure
In topology, the closure of a subset S of a topological space is often denoted S or .
Improper rotation
In crystallography, an overline indicates an improper rotation or a negative number:
- is the Hermann–Mauguin notation for a threefold rotoinversion, used in crystallography.
- is the direction with Miller indices , , .
Maximal conductance
In
Antiparticles
Overlines are used in subatomic particle physics to denote antiparticles for some particles (with the alternate being distinguishing based on electric charge). For example, the proton is denoted as
p
, and its corresponding antiparticle is denoted as
p
.
Engineering
An
Morse (CW)
Some Morse code prosigns can be expressed as two or three characters run together, and an overline is often used to signify this. The most famous is the distress signal, SOS.
Writing
An overline-like symbol is traditionally used in Syriac text to mark abbreviations and numbers. It has dots at each end and the center. In German it is occasionally used to indicate a pair of letters which cannot both be fitted into the available space.[9][10]
When Morse code is written out as text, overlines are used to distinguish prosigns and other concatenated character groups from strings of individual characters.
In
![Overlines used in a version of the Bible in Persian (1920)](http://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Persian_Bible_overline.png/300px-Persian_Bible_overline.png)
Linguistics
X-bar theory derives its name from the overbar. One of the core proposals of the theory was the creation of an intermediate syntactic node between phrasal (XP) and unit (X) levels; rather than introduce a different label, the intermediate unit was marked with a bar.
Implementations
HTML with CSS
In
<span style="text-decoration: overline">text</span>
results in: text.
The text decoration property supports also other typographical features with horizontal lines:
Unicode
Unicode includes two graphic characters, U+00AF ¯ MACRON and U+203E ‾ OVERLINE. They are compatibility equivalent to the U+0020 SPACE with non-spacing diacritics U+0304 ◌̄ COMBINING MACRON and U+0305 ◌̅ COMBINING OVERLINE respectively; the latter allows an overline to be placed over any character. There is also U+033F ◌̿ COMBINING DOUBLE OVERLINE. As with any combining character, it appears in the same character box as the character that logically precedes it: for example, x̅, compared to x‾. A series of overlined characters, for example 1̅2̅3̅, may result either in a broken or an unbroken line, depending on the font.
In Unicode, character U+FE26 COMBINING CONJOINING MACRON is conjoining (bridging) two characters: ◌︦◌.
In East Asian (
Unicode maps the overline-like character from ISO/IEC 8859-1 and code page 850 to the U+00AF ¯ MACRON symbol mentioned above. In a reversal of its official name (and compatibility decomposition), it is much wider than an actual macron diacritic over most letters, and actually wider than U+203E ‾ OVERLINE in most fonts. In Microsoft Windows, U+00AF can be entered with the keystrokes Alt+0175 (where numbers are entered from the numeric keypad). In GTK, the symbol can be added using the keystrokes Ctrl+⇧ Shift+U to activate Unicode input, then type "00AF" as the code for the character. On a Mac, with the ABC Extended
keyboard, use ⌥ Option+a.
The Unicode character U+070F
The Unicode character U+0B55 ୕ ORIYA SIGN OVERLINE is used as a length mark in Odia script.
Word processors
In Microsoft Word, overstriking of text can be accomplished with the EQ \O()
field code. The field code {EQ \O(x,¯)}
produces x and the field code {EQ \O(xyz,¯¯¯)}
produces xyz. (Doesn't work in Word 2010; it is necessary to insert MS Equation object).
Windows: Alt+0773 (once before character, one more time after character).
LibreOffice has direct support for several styles of overline in its "Format / Character / Font Effects" dialog.
Overstriking of longer sections of text, such as in 123, can also be produced in many
TeX
In LaTeX, a text <text> can be overlined with $\overline{\mbox{<text>}}$
. The inner \mbox{}
is necessary to
override the math-mode (here invoked by the dollar signs) which the \overline{}
demands.
See also
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
- Ā
- Titlo, an overline used to indicate numerals or abbreviations in Cyrillic
- Underscore
References
- ^ Smith, T. P. (2013). How Big is Big and How Small is Small: The Sizes of Everything and Why.
- ^ Wells, J.C. (2001). "Orthographic diacritics and multilingual computing". University College London. Retrieved 23 March 2014.
- ^ Cappelli, Adriano (1961). Manuali Hoepli Lexicon Abbreviature Dizionario Di Abbreviature Latine ed Italiane. Milan: Editore Ulrico Hoepli Milano. p. 256.
- ^ "Line Segment Definition - Math Open Reference". www.mathopenref.com. Retrieved 2020-08-24.
- ^ "Sample Means". www.stat.yale.edu. Retrieved 2020-08-24.
- ^ "Set Operations | Union | Intersection | Complement | Difference | Mutually Exclusive | Partitions | De Morgan's Law | Distributive Law | Cartesian Product". www.probabilitycourse.com. Retrieved 2020-08-24.
- ^ Weisstein, Eric W. "Complex Conjugate". mathworld.wolfram.com. Retrieved 2020-08-24.
- PMID 12991237.
- ^ Hardwig, Florian (2011-11-23). "Gräfinnen". Flickr. Retrieved 26 December 2017.
- ^ Hardwig, Florian (2015-12-26). "Lieder zur Weihnachtszeit (1940)". Fonts in Use. Retrieved 26 December 2017.
It used to be common to mark omitted double letters with an overbar, especially for "mm" and "nn". These abbreviations come in handy when lyrics have to match the musical notes, see 'da kom[m]t er her'.
- ^ "Emphasis (typography)". Emphasis (typography). Retrieved 2020-09-02.
- ISBN 978-1-936213-02-3,
FULLWIDTH MACRON • sometimes treated as fullwidth overline