half

One half (PL: halves) is the irreducible fraction resulting from dividing one by two (2) or the fraction resulting from dividing any number by its double. 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". One half often appears 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 = base/2 × perpendicular height.One half also figures in the formula for calculating figurate numbers, such as triangular numbers and pentagonal numbers:






n
2




[


(

s
−
2

)

n
−
(
4
−
s
)

]




{\displaystyle {\frac {n}{2}}{\left[\left(s-2\right)n-(4-s)\right]}}
and in the formula for computing magic constants for magic squares





M

2


(
n
)
=


n
2



(


n

2


+
1

)



{\displaystyle M_{2}={\frac {n}{2}}\left(n^{2}+1\right)}
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 common to believe these expressions represent distinct numbers: see the proof that 0.999... equals 1 for a detailed discussion of a related case. In odd bases, one half has no terminating representation, only a single representation with a repeating fractional component, such as 0.11111111... in ternary.

You do not have permission to view the full content of this post. Log in or register now.