One half ( : halves) is the irreducible fraction resulting from dividing

one 1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. I ...

by two or the fraction resulting from dividing any number by its double.

Multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...

by one half is equivalent to division by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling". One half often appears in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts. For instance, the area ''S'' of a triangle is computed. :''S'' = × perpendicular height. One half also figures in the formula for calculating figurate numbers, such as triangular numbers and pentagonal numbers: :

\frac

and in the formula for computing magic constants for

magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...

s :

M_2(n) = \frac \left(n^ + 1\right)

The

Riemann hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in ...

states that every nontrivial complex root of the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...

has a real part equal to . One half has two different

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

expansions, the familiar 0.5 and the recurring 0.49999999... It has a similar pair of expansions in any even base. It is common to believe these expressions represent distinct numbers: see the proof that 0.999... equals 1 for a detailed discussion of a related case. In odd bases, one half has no terminating representation, only a single representation with a repeating fractional component, such as 0.11111111... in

ternary Ternary (from Latin ''ternarius'') or trinary is an adjective meaning "composed of three items". It can refer to: Mathematics and logic * Ternary numeral system, a base-3 counting system ** Balanced ternary, a positional numeral system, usef ...

Particularities in writing and language

is also one of the few fractions to usually have a key of its own on typewriters (see fractions). It also has its own code point in some early extensions of ASCII at 171 (AB_hex). In Unicode, it has its own code unit at U+00BD (decimal 189) in the C1 Controls and Latin-1 Supplement block and a cross-reference in the

Number Forms Number Forms is a Unicode block containing Unicode compatibility characters that have specific meaning as numbers, but are constructed from other characters. They consist primarily of vulgar fractions and Roman numerals. In addition to the cha ...

block, rendering as "½." The HTML entity is ½. One half is also one of the few fractions which are commonly expressed in natural languages by

suppletion In linguistics and etymology, suppletion is traditionally understood as the use of one word as the inflected form of another word when the two words are not cognate. For those learning a language, suppletive forms will be seen as "irregular" or even ...

rather than regular derivation: in English, for example, compare ''"one half"'' against other regular formations like ''"one-sixth"''. It is acceptable to write one half as a hyphenated word, "one-half" or non-hyphenated, "one half".

Code points

In the Unicode standard, the symbol ½ has the code point U+00BD ½ Vulgar Fraction One Half (HTML #0189· inherited from Latin-1)

PC entry

* + (keeping Alt pressed until all 4 digits have been typed on the numeric keypad only)

References

{{Fractions and ratios Half Rational numbers

Particularities in writing and language

Code points

PC entry

See also

References