22 (number)

22 can also read as "two twos", which is the only fixed point of John Conway's look-and-say function. In other words, "22" generates the infinite repeating sequence "22, 22, 22, ..."^[17]

Permutable and unique primes

The are 22 permutable primes in decimal:^[18]

$${\displaystyle {\begin{aligned}&(2,3,5,7),\\&(R_{2},13,17,31,37,71,73,79,97),\\&(113,131,199,311,337,373,733,919,991)\\\end{aligned}}}$$

${\displaystyle R_{19},R_{23},R_{317},R_{1031},R_{49081},\ldots }$, where ${\displaystyle R_{2}}$ represents ${\displaystyle 11.}$

The twenty-second

of ${\displaystyle 7}$, equal to ${\displaystyle 0.{\overline {142857}}.}$

Being 84 = 7 × 12 digits long with a period length of 294 = 14 × 21 digits, it is the number:

${\displaystyle 142,857,157,142,857,142,856,999,999,985,714,285,714,285,857,142,857,142,855,714,285,571,428,571,428,572,857,143.}$

The sum of all two-digit permutable primes in decimal — that are pairs, without including ${\displaystyle R_{2}}$ — is 418, which is the sum of the digits of the twenty-second unique prime in base ten (all repunit primes are unique, where 3 and 37 are permutable as well as unique).

Geometry

Polytopes

All regular polygons with ${\displaystyle n}$ < ${\displaystyle 22}$

of the form _p{a}_q{b}_r: eight are self-dual, while fourteen exist as dual polytope pairs; twenty-one belong in ${\displaystyle \mathbb {C} ^{2}}$ while one belongs in ${\displaystyle \mathbb {C} ^{3}}$.

There are twenty-two different subgroups that describe full icosahedral symmetry, that is based on the regular icosahedron. Three groups are generated by particular inversions, five groups by reflections, and nine groups by rotations, alongside three mixed groups, the pyritohedral group, and the full icosahedral group.

There are 22

• 15 Archimedean semiregular solids in 3-space, which include two chiral forms, one from the snub cube and one from the snub dodecahedron. In other words, from symmetries of 13 distinct semiregular polyhedra, two of which have mirror images.
• 3 semiregular polychora in 4-space: the rectified 5-cell, the rectified 600-cell and the snub 24-cell.
• 4
  root vectors of simple Lie group E₈
  .

The family of k₂₁ polytopes can be extended backward to include the rectified 5-cell and the three-dimensional triangular prism, which is the simplest semiregular polytope.

On the other hand,

paracompact infinite honeycomb that contains 2₂₂ Euclidean honeycomb facets under Coxeter group

symmetry ${\displaystyle {\bar {T}}_{7}}$, with 2₂₂ made of 1₂₂ facets, and so forth. The Coxeter symbol for these figures is of the form k_ij, where each letter represents a length of order-3 branches on a Coxeter–Dynkin diagram with a single ring on the end node of a k-length sequence of branches.

There are twenty-two Coxeter groups in the sixth dimension that generate uniform polytopes: four of these generate uniform non-prismatic figures, while the remaining eighteen generate uniform prisms, duoprisms and triaprisms.

Sporadic groups

The number 22 appears prominently within

The extended binary Golay code ${\displaystyle \mathbb {B} _{24}}$, which is related to Steiner system W₂₄, is constructed as a vector space of F₂ from the words:^[24]

${\displaystyle c_{j}=e({\overline {\rm {x}}})\cdot {\overline {\rm {x}}}^{j}(j=0,...,22),{\text{ }}}$ and ${\displaystyle {\text{ }}}$${\displaystyle c_{23}=\sum _{i=0}^{22}{\overline {\rm {x}}}^{i}+{\overline {\rm {x}}}^{\infty }}$

with ${\displaystyle c\in F_{2}}$, and ${\displaystyle e({\overline {\rm {x}}})}$ the quadratic residue code of the binary Golay code ${\displaystyle \mathbb {B} _{23}}$ (with ${\displaystyle {\overline {\rm {x}}}^{\infty }}$ its parity check). M₂₃ is the automorphism group of ${\displaystyle \mathbb {B} _{23}}$.

The extended ternary Golay code [12, 6, 6], whose root is the ternary Golay code [11, 6, 5] over F₃, has a complete weight enumerator value equal to:^[25]

${\displaystyle x^{12}+y^{12}+z^{12}+22\left(x^{6}y^{6}+y^{6}z^{6}+z^{6}x^{6}\right)+220\left(x^{6}y^{3}z^{3}+x^{3}y^{6}z^{3}+x^{3}y^{3}z^{6}\right).}$

Calculations for π

${\displaystyle {\frac {22}{7}}=3.14{\color {red}28}\ldots }$ is a commonly used

${\displaystyle {\sqrt[{4}]{\frac {2143}{22}}}=3.141\;592\;65{\color {red}2\;582\;\ldots }}$ from an approximate construction of the squaring of the circle by Srinivasa Ramanujan, correct to eight decimal places.^[26]

Natural logarithms of integers in binary are known to have Bailey–Borwein–Plouffe type formulae for ${\displaystyle \pi }$ for all integers ${\displaystyle n=\{1,2,3,4...,22\}}$.^[27][28]

In science

• 22 is the atomic number of titanium.
• 22 is the number of proteinogenic
  amino acids
  .
• 22 is the number of bones in the human skull: 14 belong to the facial skeleton and 8 to the neurocranium.

In aircraft

• 22 is the designation of the USAF stealth fighter, the
  F-22 Raptor
  .

In art, entertainment, and media

In music

• "Twenty Two" is a song by:
  • Karma to Burn (2007)^[29]
  • The Vicar (2013)^[30]
  • Jordan Sweeney (2008)^[31]
  • The Good Life (2000)^[32]
  • Sweet Nectar (1996)^[33]
  • American Generals (2004)^[34]
  • Dan Anderson (2007)^[35]
  • Bad Cash Quartet (2006)^[36]
  • Millencolin (1999)^[37]
  • Enter the Worship Circle (2005)^[38]
  • Blank Dogs (2008)^[39]
  • Al Candello (2002)^[40]
  • Amen Dunes (2018)^[41]
• In Jay-Z's song "22 Two's", he rhymes the words: too, to, and two, 22 times in the first verse.^[42]
• "22 Acacia Avenue" is a song by Iron Maiden on the album The Number of the Beast.^[43]
• Catch 22 is an album by death metal band Hypocrisy.^[44]
• "22" is a song by Lily Allen on the album It's Not Me, It's You.
• 22 Dreams is a song and album by Paul Weller. The album has 22 songs on it.^[45]
• The Norwegian electronica project Ugress uses 22 as a recurring theme. All four albums feature a track with 22 in the title.^[46][47][48]
• "22" is a song by Taylor Swift on her fourth album Red.^[30]
• "The Number 22" is a song by Ashbury Heights on the album The Looking Glass Society.^[49]
• 22, A Million is an album by Bon Iver. The first track of the album is called "22 (OVER SOON)".^[50]
• Cubic 22 was a Belgian techno duo.^[51]
• "22" is a song by the English alternative rock band Deaf Havana on their album Old Souls.^[52]
• "22" is a song by the Irish singer
  Eurovision 2019
  .

In other fields

• Catch-22 (1961), Joseph Heller's novel, and its 1970 film adaptation gave rise to the expression of logic "catch-22".^[54]
• Revista 22 is a magazine published in Romania.
• There are 22 stars in the Paramount Pictures logo.^[55]
• "Twenty Two" (February 10, 1961) is Season 2–episode 17 (February 10, 1961) of the 1959–1964 TV series The Twilight Zone, in which a hospitalized dancer has nightmares about a sinister nurse inviting her to Room 22, the hospital morgue.
• Traditional
  Occult Tarot decks usually have 22 similar cards which are called Major Arcana by fortune-tellers. Occultists have related this number to the 22 letters of the Hebrew alphabet and the 22 paths in the Kabbalistic Tree of Life
  .
• "22" is the number assigned to the unborn soul who serves as a prominent character in the Pixar film Soul.

In computing and technology

• 22 is the standard port number for the Secure Shell protocol.

In culture and religion

• There are 22 letters in the Hebrew alphabet.^[56]
• In the
  Sephirot
  .
• There are 22 chapters in the book: The Revelation of Jesus Christ, Book of Revelation.
• 22 is a master number in numerology.^[57]

In sports

• In both American football and association football, a total of 22 players (counting both teams) start the game, and this is also the maximum number of players that can be legally involved in play at any given time.
• In men's Australian rules football, each team is allowed a squad of 22 players (18 on the field and 4 interchanges).
• The length of a cricket pitch is 22 yards.
• In rugby union, the "22" is a line in each half of the field which is 22 meters from the respective try line. It has significance in a number of laws particularly relating to kicking the ball away.
• A snooker game (called a "frame") starts with 22 coloured balls at specified locations on the table (15 red balls and 7 others).

In weights and measures

• The number of yards in a chain.^[58]

In other uses

Twenty-two may also refer to:

• 22 is the number of the
  French department Côtes-d'Armor
• "22" is a common name for the .22 calibre .22 Long Rifle cartridge.
• In
  French
  jargon, "22" is used as a phrase to warn of the coming of the police (typically "22, v'là les flics !" (In English: "5-0! Cops!")
• In photography, f/22 is the largest f-stop (and thus smallest aperture) available on most lenses made for single-lens reflex cameras
• In
  Spanish lottery and bingo, 22 is nicknamed los dos patitos, 'the two little ducks' after its shape.^[59][60]

• Catch 22 (disambiguation)
• List of highways numbered 22
• Synchronicity^[relevant?]

References

External links

Wikimedia Commons has media related to 22 (number).

• "The Number 22 at The Database of Number Correlations". Virtuescience.