22 (number)

Short description: Natural number

| <- 21  | 22 |  23 ->

|
|

← 20 21 22 23 24 25 26 27 28 29 →

List of numbers — Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal| twenty-two
Ordinal| 22nd
(twenty-second)
Factorization| 2 × 11
Divisors| 1, 2, 11, 22
Greek numeral| ΚΒ´
Roman numeral| XXII
Binary| 101102
Ternary| 2113
Quaternary| 1124
Quinary| 425
Senary| 346
Octal| 268
Duodecimal| 1A12
Hexadecimal| 1616
Vigesimal| 1220
Base 36| M36

22 (twenty-two) is the natural number following 21 and preceding 23.

## Contents

* 1 In mathematics
* 2 In science
* 3 In aircraft
* 4 In art, entertainment, and media
* 4.1 In music
* 4.2 In other fields
* 5 In computing and technology
* 6 In culture and religion
* 7 In sports
* 8 In weights and measures
* 9 In other uses
* 10 See also
* 11 References
* 12 External links

## In mathematics

The first 22 numbers can be arranged on a graph such that select sums between two numbers in the set yield all primes from 3 to 43. The graph has near-perfect vertical and horizontal reflective symmetry.[1]

22 is a palindromic number.[2][3] It is the second Smith number, the second Erdős–Woods number, and the fourth large Schröder number.[4][5][6] It is also a Perrin number, from a sum of 10 and 12.[7]

22 is the sixth distinct semiprime,[8] and the fourth of the form 2×q where q is a higher prime. It is the second member of the second cluster of discrete biprimes (21, 22), where the next such cluster is (38, 39). It contains an aliquot sum of 14 (itself semiprime), within an aliquot sequence of four composite numbers (22, 14, 10, 8, 7, 1, 0) that are rooted in the prime 7-aliquot tree.

The maximum number of regions into which five intersecting circles divide the plane is 22.[9] 22 is also the quantity of pieces in a disc that can be created with six straight cuts, which makes 22 the seventh central polygonal number.[10][11]

22 is the fourth pentagonal number, the third hexagonal pyramidal number, and the third centered heptagonal number.[12][13][14]

227 is a commonly used approximation of the irrational number π, the ratio of the circumference of a circle to its diameter, where in particular 22 and 7 are consecutive hexagonal pyramidal numbers. Also,

2143224=3.141592652582… from an approximate construction of the squaring of the circle by Srinivasa Ramanujan, correct to eight decimal places.[15]

Natural logarithms of integers in binary are known to have Bailey–Borwein–Plouffe type formulae for π for all integers n={1,2,3,4...,22}.[16][17]

22 is the number of partitions of 8, as well as the sum of the totient function over the first eight integers, with φ(n) for 22 returning 10.[18][19]

22 can 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, ..."[20]

All regular polygons with n < 22 edges can be constructed with an angle trisector, with the exception of the 11-sided hendecagon.[21]

There is an elementary set of twenty-two single-orbit convex tilings that tessellate two-dimensional space with face-transitive, edge-transitive, and/or vertex-transitive properties: eleven of these are regular and semiregular Archimedean tilings, while the other eleven are their dual Laves tilings. Twenty-two edge-to-edge star polygon tilings exist in the second dimension that incorporate regular convex polygons: eighteen involve specific angles, while four involve angles that are adjustable.[22] Finally, there are also twenty-two regular complex apeirohedra of the form p{a}q{b}r: eight are self-dual, while fourteen exist as dual polytope pairs; twenty-one belong in ℂ2 while one belongs in ℂ3.[23]

There are twenty-two different subgroups that describe full icosahedral symmetry. 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 finite semiregular polytopes through the eighth dimension, aside from the infinite families of prisms and antiprisms in the third dimension and inclusive of 2 enantiomorphic forms. Defined as vertex-transitive polytopes with regular facets, there are:

* 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 semiregular polytopes from 5-space through 8-space that are part of the family of k21 polytopes: the demipenteract, 221, 321, and 421; with the final figure representing the 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, k22 polytopes are a family of five different polytopes up through the eighth dimension, that include three finite polytopes and two honeycombs. Its root figure is the first proper duoprism, the 3-3 duoprism (-122), which is made of six triangular prisms. The second figure is the birectified 5-simplex (022), and the last finite figure is the 6th-dimensional 122 polytope. 122 is highly symmetric, whose 72 vertices represent the root vectors of the simple Lie group E6. 322 is a paracompact infinite honeycomb that contains 222 Euclidean honeycomb facets under Coxeter group symmetry T¯7, with 222 made of 122 facets, and so forth. The Coxeter symbol for these figures is of the form kij, 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.

The number 22 appears prominently within sporadic groups. Mathieu group M22 is one of 26 such sporadic finite simple groups, defined as the 3-transitive permutation representation on 22 points. It is the monomial of the McLaughlin sporadic group, McL, and the unique index 2 subgroup of the automorphism group of Steiner system S(3,6,22).[24] Mathieu group M23 contains M22 as a point stabilizer, and has a minimal irreducible complex representation in 22 dimensions, like McL. M23 has two rank 3 actions on 253 points, with 253 equal to the sum of the first 22 non-zero positive integers, or the 22nd triangular number. Both M22 and M23 are maximal subgroups within Mathieu group M24, which works inside the lexicographic generation of Steiner system S(5,8,24) W24, where single elements within 759 octads of 24-element sets occur 253 times throughout its entire set. On the other hand, the Higman–Sims sporadic group HS also has a minimal faithful complex representation in 22 dimensions, and is equal to 100 times the group order of M22, |HS| = 100|M22|. Conway group Co1 and Fischer group Fi24 both have 22 different conjugacy classes.

The extended binary Golay code 𝔹24, which is related to Steiner system W24, is constructed as a vector space of F2 from the words:[25]

cj=e(x‾)⋅x‾j(j=0,...,22), and  c23=∑i=022x‾i+x‾∞

with c∈F2, and e(x‾) the quadratic residue code of the binary Golay code 𝔹23 (with x‾∞ its parity check). M23 is the automorphism group of 𝔹23.

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:[26]

x12+y12+z12+22(x6y6+y6z6+z6x6)+220(x6y3z3+x3y6z3+x3y3z6).

The 22nd unique prime in base ten is notable for having starkly different digits compared to its preceding (and latter) unique primes, as well as for the similarity of its digits to those of the reciprocal of 7 (0.142857‾). Being 84 digits long with a period length of 294 digits, it is the number:[27]

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

## 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)[28]
* The Vicar (2013)[29]
* Jordan Sweeney (2008)[30]
* The Good Life (2000)[31]
* Sweet Nectar (1996)[32]
* American Generals (2004)[33]
* Dan Anderson (2007)[34]
* Bad Cash Quartet (2006)[35]
* Millencolin (1999)[36]
* Enter the Worship Circle (2005)[37]
* Blank Dogs (2008)[38]
* Al Candello (2002)[39]
* Amen Dunes (2018)[40]
* In Jay-Z's song "22 Two's", he rhymes the words: too, to, and two, 22 times in the first verse.[41]
* "22 Acacia Avenue" is a song by Iron Maiden on the album The Number of the Beast.[42]
* Catch 22 is an album by death metal band Hypocrisy.[43]
* "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.[44]
* The Norwegian electronica project Ugress uses 22 as a recurring theme. All four albums feature a track with 22 in the title.[45][46][47]
* "22" is a song by Taylor Swift on her fourth album Red.[29]
* "The Number 22" is a song by Ashbury Heights on the album The Looking Glass Society.[48]
* 22, A Million is an album by Bon Iver. The first track of the album is called "22 (OVER SOON)".[49]
* Cubic 22 was a Belgian techno duo.[50]
* "22" is a song by the English alternative rock band Deaf Havana on their album Old Souls.[51]
* "22" is a song by the Irish singer Sarah McTernan.[52] She represented Ireland with this song at 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".[53]
* Revista 22 is a magazine published in Romania.
* There are 22 stars in the Paramount Pictures logo.[54]
* "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 Tarot decks have 22 cards with allegorical subjects. These serve as trump cards in the game. The Fool is usually a kind of wild-card among the trumps and unnumbered, so the highest trump is numbered 21. 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.[55]
* In the Kabbalah, there are 22 paths between the Sephirot.
* There are 22 chapters in the book: The Revelation of Jesus Christ, Book of Revelation.
* 22 is a master number in numerology.[56]

## 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.[57]

## 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.[58][59]

## See also

* Catch 22 (disambiguation)
* List of highways numbered 22
* Synchronicity[relevant? - discuss]

## References

1. ↑ Barton, James. "The Number 22: Properties and Meanings". https://www.virtuescience.com/22.html.
2. ↑ Sloane, N. J. A., ed. "Sequence A002113 (Palindromes in base 10)". OEIS Foundation. https://oeis.org/A002113. Retrieved 2022-04-16.
3. ↑ Weisstein, Eric W.. "Semiprime" (in en). https://mathworld.wolfram.com/Semiprime.html.
4. ↑ Sloane, N. J. A., ed. "Sequence A006753 (Smith numbers)". OEIS Foundation. https://oeis.org/A006753. Retrieved 2016-05-31.
5. ↑ Sloane, N. J. A., ed. "Sequence A059756 (Erdős-Woods numbers)". OEIS Foundation. https://oeis.org/A059756. Retrieved 2016-05-31.
6. ↑ Sloane, N. J. A., ed. "Sequence A006318 (Large Schröder numbers)". OEIS Foundation. https://oeis.org/A006318. Retrieved 2022-06-01.
7. ↑ Sloane, N. J. A., ed. "Sequence A001608 (Perrin sequence)". OEIS Foundation. https://oeis.org/A001608. Retrieved 2016-05-31.
8. ↑ Sloane, N. J. A., ed. "Sequence A001358". OEIS Foundation. https://oeis.org/A001358.
9. ↑ Sloane, N. J. A., ed. "Sequence A014206". OEIS Foundation. https://oeis.org/A014206. Retrieved 2022-04-16.
10. ↑ Sloane, N. J. A., ed. "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence))". OEIS Foundation. https://oeis.org/A000124. Retrieved 2016-05-31.
11. ↑ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1986): 31
12. ↑ Sloane, N. J. A., ed. "Sequence A000326 (Pentagonal numbers)". OEIS Foundation. https://oeis.org/A000326. Retrieved 2016-05-31.
13. ↑ Sloane, N. J. A., ed. "Sequence A069099 (Centered heptagonal numbers)". OEIS Foundation. https://oeis.org/A069099. Retrieved 2016-05-31.
14. ↑ Sloane, N. J. A., ed. "Sequence A002412 (Hexagonal pyramidal numbers, or greengrocer's numbers)". OEIS Foundation. https://oeis.org/A002412. Retrieved 2022-04-16.
15. ↑ Ramanujan, S. (1914). "Modular equations and approximations to π". Quarterly Journal of Mathematics 45: 350–372. http://ramanujan.sirinudi.org/Volumes/published/ram06.pdf.π&rft.jtitle=[[Quarterly+Journal+of+Mathematics]]&rft.aulast=Ramanujan&rft.aufirst=S.&rft.au=Ramanujan, S.&rft.date=1914&rft.volume=45&rft.pages=350–372&rft_id=http://ramanujan.sirinudi.org/Volumes/published/ram06.pdf&rfr_id=info:sid/en.wikibooks.org:22_(number)">
16. ↑ Bailey, David H.; Borwein, Peter B.; Plouffe, Simon (1997). "On the Rapid Computation of Various Polylogarithmic Constants". Mathematics of Computation 66 (218): 905. doi:10.1090/S0025-5718-97-00856-9.
17. ↑ Chamberland, Marc (2003). "Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes". Journal of Integer Sequences 6 (3.3.7): 5. Bibcode: 2003JIntS...6...37C. https://chamberland.math.grinnell.edu/papers/bbp.pdf.
18. ↑ Sloane, N. J. A., ed. "Sequence A002088 (Sum of totient function)". OEIS Foundation. https://oeis.org/A002088. Retrieved 2016-05-31.
19. ↑ Sloane, N. J. A., ed. "Sequence A000010 (Euler totient function phi(n))". OEIS Foundation. https://oeis.org/A000010. Retrieved 2022-04-16.
20. ↑ Sloane, N. J. A., ed. "Sequence A010861 (Look-and-say constant sequence 22)". OEIS Foundation. https://oeis.org/A010861. Retrieved 2022-07-21.
21. ↑ Gleason, Andrew M. (1988). "Angle trisection, the heptagon, and the triskaidecagon". American Mathematical Monthly (Taylor & Francis, Ltd) 95 (3): 191–194. doi:10.2307/2323624. https://www.tandfonline.com/doi/abs/10.1080/00029890.1988.11971989?journalCode=uamm20.
22. ↑ Tilings and Patterns Branko Gruenbaum, G.C. Shephard, 1987. 2.5 Tilings using star polygons, pp.82-85.
23. ↑ Coxeter, H.S.M. (1991), Regular Complex Polytopes, Cambridge University Press, p. 140, ISBN 0-521-39490-2
24. ↑ Weisstein, Eric W.. "Mathieu Groups" (in en). https://mathworld.wolfram.com/MathieuGroups.html.
25. ↑ Bernhardt, Frank; Landrock, Peter; Manz, Olaf (1990). "The Extended Golay Codes Considered as Ideals". Journal of Combinatorial Theory. Series A 55 (2): 237. doi:10.1016/0097-3165(90)90069-9.
26. ↑ Ostergard, Patrick R. K.; Svanstrom, Mattias (2002). "Ternary Constant Weight Codes". The Electronic Journal of Combinatorics 9: 13 (R41). doi:10.37236/1657.
27. ↑ Sloane, N. J. A., ed. "Sequence A040017 (Unique period primes)". OEIS Foundation. https://oeis.org/A040017. Retrieved 2022-05-20.
28. ↑ (in en-us) Twenty Two – Karma to Burn | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0009893222, retrieved 2020-08-12
29. ↑ 29.0 29.1 (in en-us) Twenty Two – The Vicar | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0047423430, retrieved 2020-08-12
30. ↑ (in en-us) Twenty Two – Jordan Sweeney | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0018931285, retrieved 2020-08-12
31. ↑ (in en-us) Twenty Two – The Good Life | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0000400024, retrieved 2020-08-12
32. ↑ (in en-us) Twenty Two – Sweet Nectar | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0011636213, retrieved 2020-08-12
33. ↑ (in en-us) Twenty Two – American Generals | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0026625646, retrieved 2020-08-12
34. ↑ (in en-us) Twenty Two – Dan Anderson | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0015889346, retrieved 2020-08-12
35. ↑ (in en-us) Twenty Two – Bad Cash Quartet | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0042010166, retrieved 2020-08-12
36. ↑ (in en-us) Twenty Two – Millencolin | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0011412943, retrieved 2020-08-12
37. ↑ (in en-us) Twenty Two – Enter the Worship Circle | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0016541714, retrieved 2020-08-12
38. ↑ (in en-us) Twenty Two – Blank Dogs | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0041159891, retrieved 2020-08-12
39. ↑ (in en-us) Twenty Two – Al Candello | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0029968870, retrieved 2020-08-12
40. ↑ (in en-us) Twenty Two – Amen Dunes | Song Info | AllMusic, https://www.allmusic.com/song/twenty-two-mt0056357812, retrieved 2020-08-12
41. ↑ (in en-us) 22 Two's – Jay-Z | Song Info | AllMusic, https://www.allmusic.com/song/22-twos-mt0031319533, retrieved 2020-08-12
42. ↑ (in en-us) 22 Acacia Avenue – Iron Maiden | Song Info | AllMusic, https://www.allmusic.com/song/22-acacia-avenue-mt0004395314, retrieved 2020-08-12
43. ↑ (in en-us) Catch 22 – Hypocrisy | Songs, Reviews, Credits | AllMusic, https://www.allmusic.com/album/catch-22-mw0000658977, retrieved 2020-08-12
44. ↑ (in en-us) 22 Dreams – Paul Weller | Songs, Reviews, Credits | AllMusic, https://www.allmusic.com/album/22-dreams-mw0000790798, retrieved 2020-08-12
45. ↑ "Ugress | Album Discography" (in en-us). https://www.allmusic.com/artist/ugress-mn0001891155.
46. ↑ (in en-us) Cinematronics – Ugress | Songs, Reviews, Credits | AllMusic, https://www.allmusic.com/album/cinematronics-mw0001366179, retrieved 2020-08-12
47. ↑ (in en-us) Unicorn – Ugress | Songs, Reviews, Credits | AllMusic, https://www.allmusic.com/album/unicorn-mw0001638042, retrieved 2020-08-12
48. ↑ (in en-us) Number 22 – Ashbury Heights | Song Info | AllMusic, https://www.allmusic.com/song/number-22-mt0052298912, retrieved 2020-08-12
49. ↑ (in en-us) 22, A Million – Bon Iver | Songs, Reviews, Credits | AllMusic, https://www.allmusic.com/album/22-a-million-mw0002973032, retrieved 2020-08-12
50. ↑ "Cubic 22 | Songs" (in en-us). https://www.allmusic.com/artist/cubic-22-mn0000140512.
51. ↑ (in en-us) 22 – Deaf Havana | Song Info | AllMusic, https://www.allmusic.com/song/22-mt0047631225, retrieved 2020-08-12
52. ↑ (in en-us) 22 – Sarah McTernan | Song Info | AllMusic, https://www.allmusic.com/song/22-mt0056640560, retrieved 2020-08-12
53. ↑ "Definition of CATCH-22" (in en). https://www.merriam-webster.com/dictionary/catch-22.
54. ↑ "Paramount Pictures' Logo Started as a Desktop Doodle, and Has Endured for 105 Years" (in en-US). https://www.adweek.com/brand-marketing/paramount-pictures-logo-started-as-a-desktop-doodle/.
55. ↑ González-Wippler, Migene (1991) (in en). The Complete Book of Amulets & Talismans. Llewellyn Worldwide. pp. 87. ISBN 978-0-87542-287-9. https://books.google.com/books?id=wYd-HKmn8jUC&q=22+letters+in+the+Hebrew+alphabet.&pg=PA87.
56. ↑ Sharp, Damian (2001) (in English). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN 978-1-57324-560-9.
57. ↑ "Definition of CHAIN" (in en). https://www.merriam-webster.com/dictionary/chain. "a unit of length equal to 66 feet"
58. ↑ Cuartas, Javier (1990-01-05). "La suerte de los dos patitos" (in es). El País (Oviedo). https://elpais.com/diario/1990/01/06/agenda/631580402_850215.html.
59. ↑ Sanz, Elena (26 April 2010). "Los dos patitos, la niña bonita, la mala pata..." (in es). https://www.muyinteresante.es/cultura/arte-cultura/articulo/los-dos-patitos-la-nina-bonita-la-mala-pata. "Lo más normal es que el nombre tuviera que ver con la forma del número. Por ejemplo, el 11 era las banderillas, y el 22, los dos patitos o las monjas arrodilladas."

## External links

* "The Number 22 at The Database of Number Correlations". http://www.virtuescience.com/22.html.

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