| Number: | 0.5 |
| Cardinal: | one half |
| Ordinal: | th (halfth) |
| Lang1: | Greek |
| Lang2: | Roman numerals |
| Lang3: | Egyptian hieroglyph |
| Lang4: | Hebrew |
| Lang5: | Malayalam |
| Lang6: | Chinese |
| Lang7: | Tibetan |
One half is the irreducible fraction resulting from dividing one (1) by two (2), or the fraction resulting from dividing any number by its double.
It often appears in mathematical equations, recipes, measurements, etc.
One half is one of the few fractions which are commonly expressed in natural languages by suppletion rather than regular derivation. In English, for example, compare the compound "one half" with other regular formations like "one-sixth".
A half can also be said to be one part of something divided into two equal parts. It is acceptable to write one half as a hyphenated word, one-half.
0
1
\tfrac{1}{2}
0.5
0.4\overline{9}
0.\overline{1}
0.\overline{2}
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".
A number
n
n
n\tfrac{2}}=\sqrt{n}.
A hemiperfect number is a positive integer with a half-integer abundancy index:
| \sigma(n) | |
| n |
=
| k | |
| 2 |
,
where
k
\sigma(n)
The area
T
b
h
T=
| b | |
| 2 |
x h.
One half figures in the formula for calculating figurate numbers, such as the
n
P2(n)=
| n(n+1) | |
| 2 |
;
and in the formula for computing magic constants for magic squares,
M2(n)=
| n | |
| 2 |
\left(n2+1\right).
Successive natural numbers yield the
n
M
M(n)=
| n+\sqrt{n2+4 | |
In the study of finite groups, alternating groups have order
| n! | |
| 2 |
.
By Euler, a classical formula involving pi, and yielding a simple expression:[2]
| \pi | |
| 2 |
| infty | |
| =\sum | |
| n=1 |
| (-1)\varepsilon | =1+ | |
| n |
| 1 | - | |
| 2 |
| 1 | + | |
| 3 |
| 1 | + | |
| 4 |
| 1 | - | |
| 5 |
| 1 | - | |
| 6 |
| 1 | |
| 7 |
+ … ,
where
\varepsilon(n)
p\equiv3(mod4)
n
For the gamma function, a non-integer argument of one half yields,
\Gamma(\tfrac{1}{2})=\sqrt{\pi};
while inside Apéry's constant, which represents the sum of the reciprocals of all positive cubes, there is[3] [4]
\zeta(3)=-\tfrac{1}{2}\Gamma'''(1)+\tfrac{3}{2}\Gamma'(1)\Gamma''(1)-(\Gamma'(1))3=-\tfrac{1}{2}\psi(2)(1);
with
\psi(m)(z)
m
C
l{H}
(x,y)
y>0
l{H}:=\{x+iy\midy>0; x,y\inR\}.
In differential geometry, this is the universal covering space of surfaces with constant negative Gaussian curvature, by the uniformization theorem.
B1
\pm\tfrac{1}{2}
The Riemann hypothesis is the conjecture that every nontrivial complex root of the Riemann zeta function has a real part equal to
\tfrac{1}{2}
| Align: | "left" |
| vulgar fraction one half | |
| See Also: | |
The "one-half" symbol has its own code point as a precomposed character in the Number Forms block of Unicode, rendering as .
The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment; consequently the decomposed forms or may be more appropriate.