# Overline

description character Unicode HTML
overline U+203E &oline;
&#8254;
◌̅
combining
U+0305 &#773;
macron ¯ U+00AF &macr;
&#175;
◌̄
combining
U+0304 &#772;
ˉ
spacing
U+02C9 &#713;

An overline or overbar or overscore (coined in analogy to underline and underscore, attested for mathematical notation since 1899), refers to the typographical feature of a line drawn immediately above the text, for example used to indicate Roman numerals multiplied by a thousand, or medieval sigla. Specifically, a line drawn over one symbol is a macron, and a line over a collection of symbols is a vinculum. Marking one or more words with a continuous line above the characters is also described as "overstriking".

In Unicode the overline is represented by U+203E overline, and always functions as an independent symbol. The character U+0305 ◌̅ combining overline allows an overline to be placed over any character (as with any combining character, it appears over the preceding character: for example, x̅, compared to x‾). A series of overlined characters usually results in an unbroken line, depending on the font (for example, 1̅2̅3̅).

A similar character is U+00AF ¯ macron (also called "overbar"), and also has a combining variant, U+0304 ◌̄ combining macron, as well as a spacing modifier variant, U+02C9 ˉ modifier letter macron. The macron characters are shorter than their "overline" counterparts, and a series of macron characters usually does not result in an unbroken line (for example, 1̄2̄3̄). Unlike overline, the macron is present in the ISO/IEC 8859-1 and MS-DOS Codepage 850 encodings. Depending on the context in which it is used, the overbar has different meanings. The table to the right gives a summary of the different Unicode characters.

For East Asian (CJK) computing, U+FFE3 fullwidth macron is available. Despite the name, Unicode maps this character to both the U+203E overline and the U+00AF ¯ macron.[1]

The Unicode character U+070F syriac abbreviation mark is used to mark in Syriac text a special overline with a dot at each end and the center, stretching from the position of the character to the end of the word. This line traditionally marks abbreviations and numbers. However, most computer systems do not render this line correctly or at all.

## Math and science

In mathematics, an overline is used primarily in two situations: either to indicate a line segment:

• $\overline{\rm AB}$

or repeating decimal value:

• 17 = 0.142857 = 0.1428571428571428571...

Since it is not always possible to format the number so that the overline is over a certain digit, it is often placed to the left of the digits that repeat:

• 3.¯3 = 3.3 = 3.333333333333...
• 3.12¯34 = 3.123434343434...

The overline is also used to indicate a sample mean:

• $\overline x$ is the average value of $x_i$

In set theory and some electrical engineering contexts, negation operators can be written as an overline above the term or expression to be negated.

Common set theory notation:

$\overline{A \cap B}=\overline{A} \cup \overline{B} \iff \overline{A \cup B}=\overline{A} \cap \overline{B}$

Electrical engineering notation illustrating De Morgan's Laws with the saying, "break the line, change the sign":

$\overline{A + B}=\overline{A} \cdot \overline{B} \iff \overline{A \cdot B}=\overline{A} + \overline{B} \iff \overline{AB}=\overline{A} + \overline{B} \iff \overline{A + B}$

in which implied multiplication, the times (cross) and the dot all mean logical AND, and the plus sign means logical OR.

In the repetition and negation usages, this notation is also referred to as a vinculum.

The overline notation can indicate a complex conjugate and analogous operations.

• if $x = a + ib$, then $\overline{x} = a - ib.$

In physics, an overline sometimes indicates a vector, although boldface and arrows are also commonly used:

• $\overline x=|x|\hat x$

In crystallography, an overline indicates an improper rotation or a negative number:

• $\overline 3$ is the Hermann–Mauguin notation for a threefold rotoinversion.
• $[\overline 11\overline2]$ is the direction with Miller indices $h=-1$, $k=1$, $l=-2$.

## Linguistics

X-bar theory makes use of overbar notation to indicate differing levels of syntactic structure. Certain structures are represented by adding an overbar to the unit, as in X. Due to difficulty in typesetting the overbar, the prime symbol is often used instead, as in X′. Contemporary typesetting software such as LaTeX has made typesetting overbars considerably simpler; both prime and overbar markers are accepted usages. Some variants of X-bar notation use a double-bar (or double-prime) to represent phrasal-level units.

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.

## Technical notes

• In HTML using CSS, <span style="text-decoration: overline">text</span>, results in: text
• In HTML documents, the macron can be produced with &#x304; (decimal &#772;), and the "combining overline" — with &#x305; (&#773;).
• In TeX, a single symbol can be overlined with \bar x or \bar{x}. Longer sections can be overlined with \overline{ABC}, where a space is written as "\ " and an umlaut is written as "\ddot a".
• In Microsoft Windows, the ISO/IEC 8859-1 0xAF symbol mentioned above can be added in any program with the keystrokes Alt+0175 (where numbers are entered from the numeric keypad).
• In GTK/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.
• 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.

Overstriking of longer sections of text, such as in 123, can also be produced in many text processors as text markup as a special form of understriking.

## References

1. ^ The Unicode Consortium (2012), "Halfwidth and Fullwidth Forms", The Unicode Standard 6.1, ISBN 978-1-936213-02-3, "FULLWIDTH MACRON • sometimes treated as fullwidth overline"