One half


One half
One-half.svg
prefixes hemi- (from Greek)

semi-/demi- (from Latin)

Binary 0.1 or 0.011111111111...
Decimal 0.5 or 0.499999999999...
Hexadecimal 0.8 or 0.7FFFFFFFFFFF...
Continued fraction [0; 1, 1] or [0; 2]
Single-precision

floating point

3F000000 (hex) =

00111111000000000000000000000000 (binary)

One half is the irreducible fraction resulting from dividing one by two (½), or any number by its double; multiplication by one half is equivalent to division by two. It appears often 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 = ½ × base × perpendicular height.

One half also figures in the formula for calculating figurate numbers, such as triangular numbers and pentagonal numbers:

½ × n [(s - 2) n - (4 - s)]

and in the formula for computing magic constants for magic squares

M2(n) = ½ × [n (n2 + 1 )].

The Riemann hypothesis states that every nontrivial complex root of the Riemann zeta function has a real part equal to 1/2.

One half has two different decimal expansions, the familiar 0.5 and the recurring 0.49999999... It has a similar pair of expansions in any even base. It is a common trap to believe these expressions represent distinct numbers: see the proof that 0.999... equals 1 for detailed discussion of a related case.

Particularities in writing and language

Postal stamp, Ireland, 1940: one halfpenny postage due.

½ is also one of the few fractions to get a key of its own on typewriters (see fractions). It also gets its own point in some early extensions of ASCII at 171; and in Unicode, it gets its own code point at U+00BD (decimal 189) in the C1 Controls and Latin-1 Supplement block, and a cross-reference in the Number Forms block, which contains some other fractions.

One half is as well one of the few fractions which is commonly expressed in natural languages by suppletion rather than regular derivation; compare English one half with regular formations like one sixth from six.

See also

References


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Look at other dictionaries:

  • one-half — n. one of two equal parts of a divisible whole; a half; a century and one half. Syn: half. [WordNet 1.5] …   The Collaborative International Dictionary of English

  • one-half — noun one of two equal parts of a divisible whole (Freq. 7) half a loaf half an hour a century and one half • Syn: ↑half • Hypernyms: ↑common fraction, ↑ …   Useful english dictionary

  • one half — See half …   Ballentine's law dictionary

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  • One-half-cloth — Полутканевый (о переплёте) …   Краткий толковый словарь по полиграфии

  • six of one, half a dozen of the other — see ↑six • • • Main Entry: ↑dozen six of one, half (a) dozen of the other (US) (or chiefly Brit six of one and half a dozen of the other) informal used to say that you do not see any real difference between two possible choices …   Useful english dictionary

  • Two and One-Half Mile Village — (auch Two and 1/2 Mile Village) ist ein Ort im kanadischen Yukon nordwestlich des Watson Lake, der überwiegend von Indianern bewohnt wird. Er liegt am Robert Campbell Highway, der den Ort Watson Lake mit Ross River verbindet, von wo er weiter bis …   Deutsch Wikipedia

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