One half
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Chinese 半 | | |||
Tibetan | ༪ |
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
As a word
One half is one of the few fractions which are commonly expressed in natural
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.
Mathematics
One half is a
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".
![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/70/Eye_of_Horus_square.png/175px-Eye_of_Horus_square.png)
A number raised to the power of one half is equal to the square root of ,
Properties
A
where is odd, and is the
The area of a triangle with base and altitude is computed as
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Almost_integer_in_triangle.svg/200px-Almost_integer_in_triangle.svg.png)
One half figures in the formula for calculating
and in the formula for computing magic constants for magic squares,
Successive natural numbers yield the -th metallic mean by the equation,
In the study of finite groups, alternating groups have order
By
where is the number of
For the gamma function, a non-integer argument of one half yields,
while inside Apéry's constant, which represents the sum of the reciprocals of all positive cubes, there is[5][6]
with the polygamma function of order on the complex numbers .
The upper half-plane is the set of points in the
In
The Bernoulli number has the value (its sign depending on competing conventions).
The Riemann hypothesis is the conjecture that every nontrivial complex root of the Riemann zeta function has a real part equal to .
Computer characters
½ | |
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vulgar fraction one half | |
In Unicode | U+00BD ½ VULGAR FRACTION ONE HALF |
Related | |
See also | U+00BC ¼ VULGAR FRACTION ONE QUARTER U+00BE ¾ VULGAR FRACTION THREE QUARTERS |
The "one-half" symbol has its own code point as a precomposed character in the Number Forms block of Unicode, rendering as ½.
The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment; consequently the decomposed forms 1⁄2 or 1/2 may be more appropriate.
See also
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Ireland-Stamp-1940-HalfCentPostageDue.jpg/160px-Ireland-Stamp-1940-HalfCentPostageDue.jpg)
References
- ^ Sloane, N. J. A. (ed.). "Sequence A159907 (Numbers n with half-integral abundancy index, sigma(n)/n equals k+1/2 with integer k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-07-31.
- ^ Ed Pegg Jr. (July 2000). "Commentary on weekly puzzles". Mathpuzzle. Retrieved 2023-08-17.
- ^ Weisstein, Eric W. "Almost integer". MathWorld -- A WolframAlpha Resource. Retrieved 2023-08-17.
- Euler, Leonhard (1748). Introductio in analysin infinitorum(in Latin). Vol. 1. apud Marcum-Michaelem Bousquet & socios. p. 244.
- ^ Evgrafov, M. A.; Bezhanov, K. A.; Sidorov, Y. V.; Fedoriuk, M. V.; Shabunin, M. I. (1972). A Collection of Problems in the Theory of Analytic Functions (in Russian). Moscow: Nauka. p. 263 (Ex. 30.10.1).
- S2CID 126076513.