View source for One half

{{for|the computer virus|OneHalf}}
{{redirect|Half}}
{{Short description|Irreducible fraction}}
{{Wiktionary|one half}}
{{Infobox number
| number = 0.5
| cardinal = one half
| ordinal = {{frac|1|2}}th (halfth)
|lang1=[[Greek numerals|Greek]]
|lang1 symbol={{resize|155%|'''∠'''}}
|lang2=[[Roman numerals]]
|lang2 symbol={{resize|125%|'''S'''}}
|lang3=[[Egyptian hieroglyph]]
|lang3 symbol={{resize|250%|'''𓐛'''}}
|lang4=[[Hebrew]]
|lang4 symbol={{resize|125%|חֵצִ}}
|lang5=[[Malayalam]]
|lang5 symbol={{resize|125%|൴}}
|lang6=[[Chinese numeral|Chinese]]
|lang6 symbol={{resize|125%|半}}
|lang7=[[Classical Tibetan|Tibetan]]
|lang7 symbol={{resize|175%|༪}}
}}

'''One half''' is the [[multiplicative inverse]] of [[2]]. It is an [[irreducible fraction]] with a numerator of 1 and a denominator of 2. It often appears in [[mathematical equation]]s, [[recipe]]s and [[measurement]]s.

== As a word ==
One half is one of the few fractions which are commonly expressed in natural [[language]]s by [[suppletion]] rather than regular derivation. In [[English language|English]], for example, compare the [[compound word|compound]] "one half" with other regular formations like "one-sixth".  

A ''half'' can also be said to be one part of something divided into two equal parts. It is acceptable to write one half as a [[Hyphen|hyphenated]] word, ''one-half''.

== Mathematics ==
One half is the [[rational number]] that lies midway between 0 and 1 on the [[number line]]. [[Multiplication]] by one half is equivalent to [[division by two]], or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling".

[[File:Eye of Horus square.png|thumb|175px|A [[square]] of side length [[1|one]], here dissected into [[rectangle]]s whose [[area]]s are successive [[Exponentiation|powers]] of '''one half'''.]]

A number raised to the [[Exponentiation|power]] of one half is equal to its [[square root]]. 

The area of a [[triangle]] is one half its [[Triangle#Area|base]] and [[Altitude (triangle)|altitude]] (or height).[[File:ModularGroup-FundamentalDomain.svg|350px|right|thumb|[[Fundamental region]] of the modular ''[[j-invariant]]'' in the '''[[upper half-plane]]''' (shaded <span style="color: gray;">gray</span>), with [[modular discriminant]] <math>|\tau| \ge 1</math> and <math>-\tfrac{1}{2} < \mathfrak{R}(\tau) \le \tfrac{1}{2}</math>, where <math>-\tfrac{1}{2} < \mathfrak{R}(\tau) < 0 \Rightarrow |\tau| > 1.</math> ]]

The [[gamma function]] evaluated at one half is the square root of [[pi]]. 

It has two different [[decimal representation]]s in [[base ten]], the familiar <math>0.5</math> and the [[recurring decimal|recurring]] <math>0.4\overline{9}</math>{{dubious|date=November 2024}}, with a similar pair of expansions in any even [[Base of computation|base]]; while in odd bases, one half has no [[Repeating decimal|terminating]] representation.

The [[Bernoulli number]] <math>B_{1}</math> has the value <math>\pm \tfrac {1}{2}</math> (its sign depending on competing conventions).

The [[Riemann hypothesis]] is the conjecture that every nontrivial [[complex number|complex root]] of the [[Riemann zeta function]] has a real part equal to <math>\tfrac {1}{2}</math>.

== Computer characters ==
{{Infobox symbol | align="left" 
|sign            = {{notatypo|½}}
|name           = [[vulgar fraction]] '''one half'''
|unicode        = {{unichar|00BD}}
|see also = {{unichar|00BC|nlink=quarter (disambiguation)}}<br />{{unichar|00BE|nlink=threequarters (disambiguation)}}
}}

The "one-half" symbol has its own [[code point]] as a [[precomposed character]] in the
[[Latin-1 Supplement]] <!-- Unlike most fractions, NOT in the Number Forms block! -->
block of [[Unicode]], rendering as {{char|½}}.
<!--Keyboard entry (including alt codes and typewriters) is system- and localisation-specific. It is not the function of Wikipedia to tell readers how to negotiate their own specific configuration. -->

The reduced size of this symbol may make it illegible to readers with relatively mild [[visual impairment]]; consequently the decomposed forms {{char|{{frac|2}}}} or {{char|{{sfrac|2}}}} may be more appropriate.

==See also==
[[File:Ireland-Stamp-1940-HalfCentPostageDue.jpg|thumb|160px|right|Postal stamp, Ireland, 1940: one halfpenny postage due.]]
*[[Division by two]]

==References==
{{Reflist}}

{{Fractions and ratios}}

[[Category:Fractions (mathematics)|Half]]
[[Category:Rational numbers]]