144 (number)
| ||||
---|---|---|---|---|
Cardinal | one hundred forty-four | |||
Ordinal | 144th (one hundred forty-fourth) | |||
Factorization | 24 × 32 | |||
Divisors | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 | |||
Greek numeral | ΡΜΔ´ | |||
Roman numeral | CXLIV | |||
Binary | 100100002 | |||
Ternary | 121003 | |||
Senary | 4006 | |||
Octal | 2208 | |||
Duodecimal | 10012 | |||
Hexadecimal | 9016 |
144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145.
It represents a dozen dozens, or one gross. It is the number of square inches in a square foot.
In
Mathematics
144 is the
Powers
144 is the smallest number whose fifth
A direct search on the CDC 6600 yielded
275 + 845 + 105 + 1335 = 1445
as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler that at least n nth powers are required to sum to an nth power, n > 2.
In
Another number that shares this property is 169, where , while
Geometry
A regular ten-sided
In the Leech lattice
144 is the sum of the divisors of 70: ,[14] where 70 is part of the only solution to the cannonball problem aside from the trivial solution, in-which the sum of the squares of the first twenty-four integers is equal to the square of another integer, 70 — and meaningful in the context of constructing the Leech lattice in twenty-four dimensions via the Lorentzian even unimodular lattice II25,1.[15]: pp.2–11 [16] 144 is relevant in testing whether two vectors in the
Other fields
- Sonnet 144 by William Shakespeare.
- 1:144 scale is a scale used for some scale models.
- Mahjong is usually played with a set of 144 tiles.
- The measurement, in cubits, of the wall of New Jerusalem shown by the seventh angel (Bible, Revelation 21:17). 144 also occurs in the name of Psalm 144.
References
- ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165
- MR 0163867.
- ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165
- MR 0163867.
- ^ Sloane, N. J. A. (ed.). "Sequence A000005 (d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- ^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function phi(n): count numbers less than or equal to n and relatively prime to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers: each number k on this list has more solutions to the equation phi(x) equal to k than any preceding k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ Sloane, N. J. A. (ed.). "Sequence A038369 (Numbers k such that k is equal to the product of digits of k by the sum of digits of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- Zbl 0145.04903.
- ^ Sloane, N. J. A. (ed.). "Sequence A003432 (Hadamard maximal determinant problem: largest determinant of a (real) {0,1}-matrix of order n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
- ^ Sloane, N. J. A. (ed.). "Sequence A000203 (...the sum of the divisors of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-06.
- S2CID 53005119
- ^ Sloane, N. J. A. (ed.). "Sequence A351831 (Vector in the 26-dimensional even Lorentzian unimodular lattice II_25,1 used to construct the Leech lattice.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-06.
- Zbl 0501.20013.
- Zbl 1152.11334.
- "The reader should note that each of Wilson’s frames [Wilson 82] contains three of ours, with 3 · 48 = 144 vectors, and has slightly larger stabilizer."
- ^ Sloane, N. J. A. (ed.). "Sequence A002336 (Maximal kissing number of n-dimensional laminated lattice.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-06.
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. (1987): 139–140.