Английская Википедия:84 (number)

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

In mathematics

Файл:Hepteract ortho petrie.svg
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>(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>g</math> surface divided by <math>g</math>.Шаблон:Cn

Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface <math>X</math> of genus <math>g > 1</math> will contain an automorphism group <math>\mathrm{Aut}(X) = G</math> whose order is classically bound to <math>|G| \le 84 \text { } (g - 1)</math>.[6]

There are 84 zero divisors in the 16-dimensional sedenions <math>\mathbb S</math>.[7]

In astronomy

In other fields

Файл:Vietnam in its region.svg
dial +84 for Vietnam

Eighty-four is also:

See also

References

Шаблон:Reflist

Шаблон:Integers