84 (eighty-four) is the natural number following 83 and preceding 85. It is seven dozens.
| ||||
|---|---|---|---|---|
| Cardinal | eighty-four | |||
| Ordinal | 84th (eighty-fourth) | |||
| Factorization | 22 × 3 × 7 | |||
| Divisors | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 | |||
| Greek numeral | ΠΔ´ | |||
| Roman numeral | LXXXIV | |||
| Binary | 10101002 | |||
| Ternary | 100103 | |||
| Senary | 2206 | |||
| Octal | 1248 | |||
| Duodecimal | 7012 | |||
| Hexadecimal | 5416 | |||
In mathematics
edit
84 is a semiperfect number,[1] being thrice a perfect number, and the sum of the sixth pair of twin primes .[2] It is the number of four-digit perfect powers in decimal.[3]
It is the third (or second) dodecahedral number,[4] and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28), which makes it the seventh tetrahedral number.[5]
The number of divisors of 84 is 12.[6] As no smaller number has more than 12 divisors, 84 is a largely composite number.[7]
The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits.[8]
A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.[9]
84 is the limit superior of the largest finite subgroup of the mapping class group of a genus surface divided by .[citation needed]
Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface of genus will contain an automorphism group whose order is classically bound to .[10]
84 is the thirtieth and largest for which the cyclotomic field has class number (or unique factorization), preceding 60 (that is the composite index of 84),[11] and 48.[12][13]
There are 84 zero divisors in the 16-dimensional sedenions .[14]
In astronomy
edit- Messier object M84, a magnitude 11.0 lenticular galaxy in the constellation Virgo
- The New General Catalogue object NGC 84, a single star in the constellation Andromeda
In other fields
edit
Eighty-four is also:
- The year AD 84, 84 BC, or 1984.
- The number of years in the Insular latercus, a cycle used in the past by Celtic peoples,[15] equal to 3 cycles of the Julian Calendar and to 4 Metonic cycles and 1 octaeteris
- The atomic number of polonium
- The model number of Harpoon missile
- WGS 84 - The latest revision of the World Geodetic System, a fixed global reference frame for the Earth.
- The house number of 84 Avenue Foch
- The number of the French department Vaucluse
- The code for international direct dial phone calls to Vietnam
- The town of Eighty Four, Pennsylvania
- The company 84 Lumber
- The ISBN Group Identifier for books published in Spain
- A variation of the game 42 played with two sets of dominoes.
- The film 84 Charing Cross Road (1987) starring Anne Bancroft and Anthony Hopkins
- KKNX Radio 84 in Eugene, Oregon
- The B-Side to "Up All Night" (Take That song)
- British Army term for the 84mm Carl Gustav recoilless rifle.
- How many Earth years it takes Uranus to orbit the Sun once
See also
editReferences
edit- ^ Sloane, N. J. A. (ed.). "Sequence A005835 (Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A077800 (List of twin primes {p, p+2})". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-08.
- ^ Sloane, N. J. A. (ed.). "Sequence A075308 (Number of n-digit perfect powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006566 (Dodecahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A040017 (Prime 3 followed by unique period primes (the period r of 1/p is not shared with any other prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-08.
- ^ Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers: a(n) = 2*n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Giulietti, Massimo; Korchmaros, Gabor (2019). "Algebraic curves with many automorphisms". Advances in Mathematics. 349 (9). Amsterdam, NL: Elsevier: 162–211. arXiv:1702.08812. doi:10.1016/J.AIM.2019.04.003. MR 3938850. S2CID 119269948. Zbl 1419.14040.
- ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Washington, Lawrence C. (1997). Introduction to Cyclotomic Fields. Graduate Texts in Mathematics. Vol. 83 (2nd ed.). Springer-Verlag. pp. 205–206 (Theorem 11.1). ISBN 0-387-94762-0. MR 1421575. OCLC 34514301. Zbl 0966.11047.
- ^ Sloane, N. J. A. (ed.). "Sequence A005848 (Cyclotomic fields with class number 1 (or with unique factorization))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Cawagas, Raoul E. (2004). "On the Structure and Zero Divisors of the Cayley-Dickson Sedenion Algebra". Discussiones Mathematicae – General Algebra and Applications. 24 (2). PL: University of Zielona Góra: 262–264. doi:10.7151/DMGAA.1088. MR 2151717. S2CID 14752211. Zbl 1102.17001.
- ^ Venerabilis, Beda (May 13, 2020) [731 AD]. "Historia Ecclesiastica gentis Anglorum/Liber Secundus" [The Ecclesiastical History of the English Nation/Second Book]. Wikisource (in Latin). Retrieved September 29, 2022.