22 (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, xxii
Binary	101102
Ternary	2113
Senary	346
Octal	268
Duodecimal	1A12
Hexadecimal	1616

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

In mathematics

22 is a semiprime,^[1] a Smith number, and an Erdős–Woods number.^[2]^[3] ${\frac {22}{7}}=3.14{\color {red}28}\ldots$ is a commonly used approximation of the irrational number $π$ , the ratio of the circumference of a circle to its diameter.

22 can read as "two twos", which is the only fixed point of John Conway's look-and-say function.^[4]

The number 22 appears prominently within sporadic groups. The Mathieu group M₂₂ is one of 26 sporadic finite simple groups, defined as the 3-transitive permutation representation on 22 points.^[5] There are also 22 regular complex apeirohedra.^[6]

22 has been proven to be a Lychrel number in base 2,^[7] since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after $4n$ steps it reaches a number consisting of 10, followed by $n + 1$ ones, followed by 01, followed by $n + 1$ zeros. This number obviously cannot be a palindrome, and none of the other numbers in the sequence are palindromes.

In other fields

Catch-22 (1961), Joseph Heller's novel, and its 1970 film adaptation gave rise to the expression of logic "catch-22".^[8]
22 equal temperament is a popular microtonal tuning temperament due to its good approximation of harmonic intervals, especially septimal intervals.

In culture and religion

22 is a master number in numerology.^[9]
There are 22 colored properties on a traditional Monopoly board.
There are 22 cards in the Major Arcana suit of a traditional tarot card deck, though they are often numbered 0-21.

In weights and measures

The number of yards in a chain.^[10]

In other uses

Twenty-two may also refer to:

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 Spanish lottery and bingo, 22 is nicknamed los dos patitos, 'the two little ducks' after its shape.^[11]^[12]

References

^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
^ Sloane, N. J. A. (ed.). "Sequence A059756 (Erdős-Woods numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
^ Sloane, N. J. A. (ed.). "Sequence A010861 (Look-and-say constant sequence 22)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-21.
^ Weisstein, Eric W. "Mathieu Groups". mathworld.wolfram.com. Retrieved 2022-07-02.
^ Coxeter, H.S.M. (1991), Regular Complex Polytopes, Cambridge University Press, p. 140, ISBN 0-521-39490-2
^ Sloane, N. J. A. (ed.). "Sequence A060382". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ "Definition of CATCH-22". www.merriam-webster.com. Retrieved 2020-08-12.
^ Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN 978-1-57324-560-9.
^ "Definition of CHAIN". www.merriam-webster.com. Retrieved 2020-08-19. a unit of length equal to 66 feet
^ Cuartas, Javier (1990-01-05). "La suerte de los dos patitos" [The luck of the two little ducks]. El País (in Spanish). Oviedo. Retrieved 17 September 2020.
^ Sanz, Elena (26 April 2010). "Los dos patitos, la niña bonita, la mala pata..." Muy Interesante (in Spanish). Retrieved 17 September 2020. 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". Virtuescience.

[1] Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[2] Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.

[3] Sloane, N. J. A. (ed.). "Sequence A059756 (Erdős-Woods numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.

[4] Sloane, N. J. A. (ed.). "Sequence A010861 (Look-and-say constant sequence 22)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-21.

[5] Weisstein, Eric W. "Mathieu Groups". mathworld.wolfram.com. Retrieved 2022-07-02.

[6] Coxeter, H.S.M. (1991), Regular Complex Polytopes, Cambridge University Press, p. 140, ISBN 0-521-39490-2

[7] Sloane, N. J. A. (ed.). "Sequence A060382". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[8] "Definition of CATCH-22". www.merriam-webster.com. Retrieved 2020-08-12.

[9] Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN 978-1-57324-560-9.

[10] "Definition of CHAIN". www.merriam-webster.com. Retrieved 2020-08-19. a unit of length equal to 66 feet

[Cuartas-11] Cuartas, Javier (1990-01-05). "La suerte de los dos patitos" [The luck of the two little ducks]. El País (in Spanish). Oviedo. Retrieved 17 September 2020.

[Sanz-12] Sanz, Elena (26 April 2010). "Los dos patitos, la niña bonita, la mala pata..." Muy Interesante (in Spanish). Retrieved 17 September 2020. 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.

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