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 divisors than 1 (and −1, when negative numbers are considered). I ...

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 Multiplication sign, cross symbol , by the mid-line #Notation and terminology, dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four Elementary arithmetic, elementary Op ...

by one half is equivalent to

division by two In mathematics, division by two or halving has also been called mediation or dimidiation. The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication alg ...

, 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 The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean * polygo ...

, such as

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...

s and

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...

s: :

\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 p ...

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 Recurring means occurring repeatedly and can refer to several different things: Mathematics and finance *Recurring expense, an ongoing (continual) expenditure *Repeating decimal, or recurring decimal, a real number in the decimal numeral syste ...

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 selectivel ...

s (see

fractions A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...

). It also has its own

code point In character encoding terminology, a code point, codepoint or code position is a numerical value that maps to a specific character. Code points usually represent a single grapheme—usually a letter, digit, punctuation mark, or whitespace—but ...

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 The Latin-1 Supplement (also called C1 Controls and Latin-1 Supplement) is the second Unicode block in the Unicode standard. It encodes the upper range of ISO 8859-1: 80 (U+0080) - FF (U+00FF). C1 Controls (0080–009F) are not graphic. Th ...

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 The HyperText Markup Language or HTML is the standard markup language for documents designed to be displayed in a web browser. It can be assisted by technologies such as Cascading Style Sheets (CSS) and scripting languages such as JavaS ...

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 humans communicate, and may be conveyed through a variety of ...

s 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 English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ...

, 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 One half ( : halves) is the irreducible fraction 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, ...

Rational numbers

Particularities in writing and language

Code points

PC entry

See also

References