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One half is one of the few fractions which are commonly expressed in naturallanguages bysuppletion rather than regular derivation. InEnglish, for example, compare thecompound "one half" with other regular formations like "one-sixth".

Ahalf can also be said to be one part of something divided into two equal parts. It is acceptable to write one half as ahyphenated word,one-half.

Mathematics

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One half is therational number that lies midway between 0 and 1 on thenumber line.Multiplication by one half is equivalent todivision by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling".

Asquare of side lengthone, here dissected intorectangles whoseareas are successivepowers ofone half.

A number raised to thepower of one half is equal to itssquare root.

The area of atriangle is one half itsbase andaltitude (or height).

Fundamental region of the modularj-invariant in theupper half-plane (shadedgray), withmodular discriminant $|\tau |\geq 1$ and $-{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )\leq {\tfrac {1}{2}}$ , where $-{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )<0\Rightarrow |\tau |>1.$

{\displaystyle |\tau |\geq 1} — Fundamental region of the modularj-invariant in theupper half-plane (shadedgray), withmodular discriminant $|\tau |\geq 1$ and $-{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )\leq {\tfrac {1}{2}}$ , where $-{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )<0\Rightarrow |\tau |>1.$

Thegamma function evaluated at one half is the square root ofpi.

It has two differentdecimal representations inbase ten, the familiar $0.5 {\displaystyle 0.5}$ and therecurring $0.4{\overline {9}}$ ^{[dubious –discuss]}, with a similar pair of expansions in any evenbase; while in odd bases, one half has noterminating representation.

TheBernoulli number $B_{1}$ has the value $\pm {\tfrac {1}{2}}$ (its sign depending on competing conventions).

TheRiemann hypothesis is the conjecture that every nontrivialcomplex root of theRiemann zeta function has a real part equal to ${\tfrac {1}{2}}$ .

Computer characters

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½
vulgar fractionone half
In Unicode	U+00BD ½VULGAR FRACTION ONE HALF
Related
See also	U+00BC ¼VULGAR FRACTION ONE QUARTER U+00BE ¾VULGAR FRACTION THREE QUARTERS

The "one-half" symbol has its owncode point as aprecomposed character in theLatin-1 Supplement block ofUnicode, rendering as½.

The reduced size of this symbol may make it illegible to readers with relatively mildvisual impairment; consequently the decomposed forms1⁄2 or⁠1/2⁠ may be more appropriate.

References

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v t e Fractions andratios
	Division and ratio	Dividend ÷Divisor =Quotient
	Fraction	⁠Numerator/Denominator⁠ = Quotient
	Algebraic Aspect Binary Continued Decimal Dyadic Egyptian Golden Silver Integer Irreducible Reduction Just intonation LCD Musical interval Paper size Percentage Unit

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