84 (number)

From HandWiki
Short description: Natural number
← 83 84 85 →
Cardinaleighty-four
Ordinal84th
(eighty-fourth)
Factorization22 × 3 × 7
Divisors1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Greek numeralΠΔ´
Roman numeralLXXXIV
Binary10101002
Ternary100103
Quaternary11104
Quinary3145
Senary2206
Octal1248
Duodecimal7012
Hexadecimal5416
Vigesimal4420
Base 362C36

84 (eighty-four) is the natural number following 83 and preceding 85.

In mathematics

A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.

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

In other fields

dial +84 for Vietnam

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

  1. 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. 
  2. Sloane, N. J. A., ed. "Sequence A077800 (List of twin primes {p, p+2})". OEIS Foundation. https://oeis.org/A077800. Retrieved 2023-06-08. 
  3. Sloane, N. J. A., ed. "Sequence A006566 (Dodecahedral numbers)". OEIS Foundation. https://oeis.org/A006566. Retrieved 2023-06-08. 
  4. "Sloane's A000292 : Tetrahedral numbers". OEIS Foundation. https://oeis.org/A000292. 
  5. 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. 
  6. 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. 
  7. 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. 
  8. Venerabilis, Beda (May 13, 2020). "Historia Ecclesiastica gentis Anglorum/Liber Secundus" (in la). https://la.wikisource.org/wiki/Historia_Ecclesiastica_gentis_Anglorum/Liber_Secundus.