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One half
From Wikipedia, the free encyclopedia
| 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 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 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.
One half is also:
- One of the few fractions to get a key of its own on typewriters. It also gets its own point in some early extensions of ASCII at 171; and in Unicode, it gets its own code point at 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 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.