One half ( : halves) is the

irreducible fraction An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisor In mathematics Mathematics is an area of kno ...

resulting from dividing one by two or the fraction resulting from dividing any number by its double. 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". 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 The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ( zeta), is a mathematical function of a complex varia ...

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 number A number is a mathematical object used to count, measure, and ...

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.

Particularities in writing and language

is also one of the few fractions to usually have a key of its own on

typewriter A typewriter is a mechanical or electromechanical machine for typing characters. Typically, a typewriter has an array of keys, and each one causes a different single character to be produced on paper by striking an inked ribbon selecti ...

s (see fractions). It also has its own code point in some early extensions of ASCII at 171 (AB_hex). In

Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...

, 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 block, rendering as "½." The

HTML The HyperText Markup Language or HTML is the standard markup language Markup language refers to a text-encoding system consisting of a set of symbols inserted in a text document to control its structure, formatting, or the relationship ...

entity is ½. One half is also one of the few fractions which are commonly expressed in natural

language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which human Humans (''Homo sapiens'') are the most abundant ...

s by suppletion 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