84 (number)
| ||||
|---|---|---|---|---|
| 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 | |||
| Quaternary | 11104 | |||
| Quinary | 3145 | |||
| Senary | 2206 | |||
| Octal | 1248 | |||
| Duodecimal | 7012 | |||
| Hexadecimal | 5416 | |||
| Vigesimal | 4420 | |||
| Base 36 | 2C36 | |||
84 (eighty-four) is the natural number following 83 and preceding 85.
In mathematics
84 is a semiperfect number,[1] being thrice a perfect number, and the sum of the sixth pair of twin primes [math]\displaystyle{ (41 + 43) }[/math].[2]
It is the third (or second) dodecahedral number,[3] and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28, 36), which makes it the sixth tetrahedral number.[4]
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.[5]
A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.
84 is the limit superior of the largest finite subgroup of the mapping class group of a genus [math]\displaystyle{ g }[/math] surface divided by [math]\displaystyle{ g }[/math].[citation needed]
Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface [math]\displaystyle{ X }[/math] of genus [math]\displaystyle{ g \gt 1 }[/math] will contain an automorphism group [math]\displaystyle{ \mathrm{Aut}(X) = G }[/math] whose order is classically bound to [math]\displaystyle{ |G| \le 84 \text { } (g - 1) }[/math].[6]
There are 84 zero divisors in the 16-dimensional sedenions [math]\displaystyle{ \mathbb S }[/math].[7]
In astronomy
- 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
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,[8] 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
- The total number of Vertcoin to be released is 84 million “Vertcoin”
- The number of former National Football League player Antonio Brown
See also
- List of highways numbered 84
References
- ↑ Sloane, N. J. A., ed. "Sequence A005835 (Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n.)". OEIS Foundation. https://oeis.org/A005835. Retrieved 2023-06-08.
- ↑ Sloane, N. J. A., ed. "Sequence A077800 (List of twin primes {p, p+2})". OEIS Foundation. https://oeis.org/A077800. Retrieved 2023-06-08.
- ↑ Sloane, N. J. A., ed. "Sequence A006566 (Dodecahedral numbers)". OEIS Foundation. https://oeis.org/A006566. Retrieved 2023-06-08.
- ↑ "Sloane's A000292 : Tetrahedral numbers". OEIS Foundation. https://oeis.org/A000292.
- ↑ 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))". OEIS Foundation. https://oeis.org/A040017. Retrieved 2023-06-08.
- ↑ Giulietti, Massimo; Korchmaros, Gabor (2019). "Algebraic curves with many automorphisms". Advances in Mathematics (Amsterdam, NL: Elsevier) 349 (9): 162–211. doi:10.1016/J.AIM.2019.04.003. https://www.sciencedirect.com/science/article/abs/pii/S0001870819301641.
- ↑ Cawagas, Raoul E. (2004). "On the Structure and Zero Divisors of the Cayley-Dickson Sedenion Algebra". Discussiones Mathematicae – General Algebra and Applications (PL: University of Zielona Góra) 24 (2): 262–264. doi:10.7151/DMGAA.1088. https://www.dmgaa.uz.zgora.pl/publish/article.php?doi=1088.
- ↑ Venerabilis, Beda (May 13, 2020). "Historia Ecclesiastica gentis Anglorum/Liber Secundus" (in la). https://la.wikisource.org/wiki/Historia_Ecclesiastica_gentis_Anglorum/Liber_Secundus.
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