Editing One half (section)

== Mathematics ==
One half is the [[rational number]] that lies midway between 0 and 1 on the [[number line]]. [[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".

[[File:Eye of Horus square.png|thumb|175px|A [[square]] of side length [[1|one]], here dissected into [[rectangle]]s whose [[area]]s are successive [[Exponentiation|powers]] of '''one half'''.]]

A number raised to the [[Exponentiation|power]] of one half is equal to its [[square root]]. 

The area of a [[triangle]] is one half its [[Triangle#Area|base]] and [[Altitude (triangle)|altitude]] (or height).[[File:ModularGroup-FundamentalDomain.svg|350px|right|thumb|[[Fundamental region]] of the modular ''[[j-invariant]]'' in the '''[[upper half-plane]]''' (shaded <span style="color: gray;">gray</span>), with [[modular discriminant]] <math>|\tau| \ge 1</math> and <math>-\tfrac{1}{2} < \mathfrak{R}(\tau) \le \tfrac{1}{2}</math>, where <math>-\tfrac{1}{2} < \mathfrak{R}(\tau) < 0 \Rightarrow |\tau| > 1.</math> ]]

The [[gamma function]] evaluated at one half is the square root of [[pi]]. 

It has two different [[decimal representation]]s in [[base ten]], the familiar <math>0.5</math> and the [[recurring decimal|recurring]] <math>0.4\overline{9}</math>{{dubious|date=November 2024}}, with a similar pair of expansions in any even [[Base of computation|base]]; while in odd bases, one half has no [[Repeating decimal|terminating]] representation.

The [[Bernoulli number]] <math>B_{1}</math> has the value <math>\pm \tfrac {1}{2}</math> (its sign depending on competing conventions).

The [[Riemann hypothesis]] is the conjecture that every nontrivial [[complex number|complex root]] of the [[Riemann zeta function]] has a real part equal to <math>\tfrac {1}{2}</math>.