One half: Difference between revisions
imported>Neutron Jack ½ is in the Latin-1 Supplement Unicode block, not Number Forms. |
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'''One half''' is the [[multiplicative inverse]] of [[2]]. It is an [[irreducible fraction]] with a numerator of 1 and a denominator of 2. It often appears in [[mathematical equation]]s, [[recipe]]s and [[measurement]]s. | '''One half''' is the [[multiplicative inverse]] of [[2]]. It is an [[irreducible fraction]] with a numerator of 1 and a denominator of 2. It often appears in [[mathematical equation]]s, [[recipe]]s and [[measurement]]s. | ||
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[[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'''.]] | [[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]]. | A number raised to the [[Exponentiation|power]] of one half is equal to its [[square root]]. This follows from the fact that when multiplying powers, the exponents add. So, <math>a^{1/2}</math> times itself is <math>a^{1/2 + 1/2}</math> which is <math>a^1</math>, which equals <math>a</math>. | ||
The area of a [[triangle]] is one half its [[Triangle#Area|base]] and [[Altitude (triangle)|altitude]] | The area of a [[triangle]] is one half its [[Triangle#Area|base]] and its height, also known as its [[Altitude (triangle)|altitude]].<ref>{{cite book|first1=Donna |last1=Kirk |display-authors=etal |year=2024 |isbn=978-1-951693-68-8 |title=Contemporary Mathematics |publisher=OpenStax |chapter=10.6 Area |chapter-url=https://openstax.org/books/contemporary-mathematics/pages/10-6-area}}</ref>[[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]]. | The [[gamma function]] evaluated at one half is the square root of [[pi]].<ref>{{cite book|first=Greg |last=Gbur |author-link=Greg Gbur |title=Mathematical Methods for Optical Physics and Engineering |year=2011 |publisher=Cambridge University Press |isbn=978-0-521-51610-5 |page=776}}</ref> | ||
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> | 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>, 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 [[Bernoulli number]] <math>B_{1}</math> has the value <math>\pm \tfrac {1}{2}</math> (its sign depending on competing conventions).<ref>{{cite book |first1=John |last1=Conway |author-link1=John Horton Conway |first2=Richard |last2=Guy |author-link2=Richard K. Guy |title=The Book of Numbers |title-link=The Book of Numbers (math book) |publisher=Springer-Verlag |date=1996 |isbn=0-387-97993-X |page=107}}</ref><ref>{{cite book|last=Arfken |first=George |date=1970 |title=Mathematical methods for physicists |edition=2nd |publisher=Academic Press |bibcode=1970mmp..book.....A |isbn=978-0120598519 |page=278}}</ref> | ||
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>. | 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>.<ref>{{cite web|url=https://www.claymath.org/millennium/riemann-hypothesis/ |title=Riemann Hypothesis |website=[[Clay Mathematics Institute]] |access-date=2025-09-12}}</ref> | ||
== Computer characters == | == Computer characters == | ||
Latest revision as of 23:39, 12 September 2025
Script error: No such module "For". Script error: No such module "redirect hatnote". Template:Short description Template:Sister project Template:Infobox number Script error: No such module "Unsubst". One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2. It often appears in mathematical equations, recipes and measurements.
As a word
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.
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".
A number raised to the power of one half is equal to its square root. This follows from the fact that when multiplying powers, the exponents add. So, times itself is which is , which equals .
The area of a triangle is one half its base and its height, also known as its altitude.[1]
The gamma function evaluated at one half is the square root of pi.[2]
It has two different decimal representations in base ten, the familiar and the recurring , with a similar pair of expansions in any even base; while in odd bases, one half has no terminating representation.
The Bernoulli number has the value (its sign depending on competing conventions).[3][4]
The Riemann hypothesis is the conjecture that every nontrivial complex root of the Riemann zeta function has a real part equal to .[5]
Computer characters
The "one-half" symbol has its own code point as a precomposed character in the Latin-1 Supplement block of Unicode, rendering as Template:Char.
The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment; consequently the decomposed forms Template:Char or Template:Char may be more appropriate.
See also
References
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