One half: Difference between revisions
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One half is as well one of the few fractions which is commonly expressed in natural [[language]]s by [[suppletion]] rather than regular derivation; compare [[English language|English]] ''one half'' with regular formations like ''one sixth'' from ''six''. |
One half is as well one of the few fractions which is commonly expressed in natural [[language]]s by [[suppletion]] rather than regular derivation; compare [[English language|English]] ''one half'' with regular formations like ''one sixth'' from ''six''. |
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==Curious properties== |
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*There are twelve ways of in which the digits 1 to 9 can be used to write a fraction equal to 1/2; 6729/13458 being the smallest, and 9327/1865 the largest. |
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*[[Riemann's Hypothesis]] states that every [[complex number|complex root]] has a real part equal to 1/2. |
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==See also== |
==See also== |
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*[[List of numbers]] |
*[[List of numbers]] |
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Revision as of 02:58, 15 January 2011
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| ½ | |
| prefixes | hemi- (from Greek) |
| 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 | 3F000000 (hex) =
00111111000000000000000000000000 (binary) |
One half is the irreducible fraction resulting from dividing one by / over two (½), or any number by its double; multiplication by one half is equivalent to division by two. It is the fraction occurring most often[citation needed] 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 )].
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
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.
Curious properties
- There are twelve ways of in which the digits 1 to 9 can be used to write a fraction equal to 1/2; 6729/13458 being the smallest, and 9327/1865 the largest.
- Riemann's Hypothesis states that every complex root has a real part equal to 1/2.
See also
 | This article about a number is a stub. You can help Wikipedia by expanding it. |