132 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred thirty-two | |||
| Ordinal | 132nd (one hundred thirty-second) | |||
| Factorization | 22 × 3 × 11 | |||
| Divisors | 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 | |||
| Greek numeral | ΡΛΒ´ | |||
| Roman numeral | CXXXII | |||
| Binary | 100001002 | |||
| Ternary | 112203 | |||
| Senary | 3406 | |||
| Octal | 2048 | |||
| Duodecimal | B012 | |||
| Hexadecimal | 8416 | |||
132 (one hundred [and] thirty-two) is the natural number following 131 and preceding 133. It is 11 dozens.
In mathematics
[edit]132 is the sixth Catalan number.[1] With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136.[2]
132 is an oblong number, as the product of 11 and 12[3] whose sum instead yields the 9th prime number 23;[4] on the other hand, 132 is the 99th composite number.[5]
Adding all two-digit permutation subsets of 132 yields the same number:
- .
132 is the smallest number in decimal with this property,[6] which is shared by 264, 396 and 35964 (see digit-reassembly number).[7]
The number of irreducible trees with fifteen vertices is 132.[8]
In a toroidal board in the n–Queens problem, 132 is the count of non-attacking queens,[9] with respective indicator of 19[10] and multiplicity of 1444 = 382 [11] (where, 2 × 19 = 38).[12]
The exceptional outer automorphism of symmetric group S6 uniquely maps vertices to factorizations and edges to partitions in the graph factors of the complete graph with six vertices (and fifteen edges) K6, which yields 132 blocks in Steiner system S(5,6,12).
In other fields
[edit]132 is also:
- OGLE-TR-132 is a magnitude 15.72 star in the star fields of the constellation Carina
- 132 Aethra is a M-type main belt asteroid
- Sonnet 132 by William Shakespeare
- The number of columns of a line printer printing in landscape mode on 14-inch paper.
- Refers to the Yo Soy 132 movement to vote in 2012 Mexican elections against PRI candidate Enrique Peña Nieto.
See also
[edit]- The year AD 132 or 132 BC
- List of highways numbered 132
References
[edit]- ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers: a(n) equal to n*(n+1).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
- ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
- ^ Sloane, N. J. A. (ed.). "Sequence A241754 (Numbers n equal to the sum of all numbers created from permutations of d digits sampled from n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A054502 (Counting sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
- ^ Sloane, N. J. A. (ed.). "Sequence A054500 (Indicator sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
- ^ Sloane, N. J. A. (ed.). "Sequence A054501 (Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
- ^ I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639. doi:10.1080/00029890.1994.11997004 JSTOR 2974691