| ||||
---|---|---|---|---|
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 | |||
Senary | 346 | |||
Octal | 268 | |||
Duodecimal | 1A12 | |||
Hexadecimal | 1616 |
22 (twenty-two) is the natural number following 21 and preceding 23.
22 is a palindromic number. [2] [3] 22 is the sixth distinct semiprime, [4] and the fourth of the form where 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.
Twenty-two is also:
22 is also a Perrin number, from a sum of 10 and 12, [13] and the second Smith number, the second Erdős–Woods number, and the fourth large Schröder number. [14] [15] [16]
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]
The are 22 permutable primes in decimal: [18]
The twenty-second 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 , equal to [19]
Being 84 = 7 × 12 digits long with a period length of 294 = 14 × 21 digits, it is the number:
The sum of all two-digit permutable primes in decimal — that are pairs, without including — 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).
All regular polygons with < edges can be constructed with an angle trisector, with the exception of the 11-sided hendecagon. [20]
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. [21] 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 while one belongs in . [22]
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 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:
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). [23] 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 , which is related to Steiner system W24, is constructed as a vector space of F2 from the words: [24]
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]
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,
Natural logarithms of integers in binary are known to have Bailey–Borwein–Plouffe type formulae for for all integers . [27] [28]
Twenty-two may also refer to:
a unit of length equal to 66 feet
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.
| ||||
---|---|---|---|---|
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 | |||
Senary | 346 | |||
Octal | 268 | |||
Duodecimal | 1A12 | |||
Hexadecimal | 1616 |
22 (twenty-two) is the natural number following 21 and preceding 23.
22 is a palindromic number. [2] [3] 22 is the sixth distinct semiprime, [4] and the fourth of the form where 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.
Twenty-two is also:
22 is also a Perrin number, from a sum of 10 and 12, [13] and the second Smith number, the second Erdős–Woods number, and the fourth large Schröder number. [14] [15] [16]
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]
The are 22 permutable primes in decimal: [18]
The twenty-second 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 , equal to [19]
Being 84 = 7 × 12 digits long with a period length of 294 = 14 × 21 digits, it is the number:
The sum of all two-digit permutable primes in decimal — that are pairs, without including — 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).
All regular polygons with < edges can be constructed with an angle trisector, with the exception of the 11-sided hendecagon. [20]
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. [21] 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 while one belongs in . [22]
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 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:
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). [23] 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 , which is related to Steiner system W24, is constructed as a vector space of F2 from the words: [24]
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]
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,
Natural logarithms of integers in binary are known to have Bailey–Borwein–Plouffe type formulae for for all integers . [27] [28]
Twenty-two may also refer to:
a unit of length equal to 66 feet
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.