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From Wikipedia, the free encyclopedia

← 43  44  45 →
Cardinalforty-four
Ordinal44th
(forty-fourth)
Factorization22 × 11
Divisors1, 2, 4, 11, 22, 44
Greek numeralΜΔ´
Roman numeralXLIV
Binary1011002
Ternary11223
Senary1126
Octal548
Duodecimal3812
Hexadecimal2C16

44 (forty-four) is the natural number following 43 and preceding 45.

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Transcription

In mathematics

Forty-four is a repdigit and palindromic number in decimal. It is the tenth 10-happy number,[1] and the fourth octahedral number.[2]

It is a square-prime of the form p2 × q, and fourth of this form and of the form 22 × q, where q is a higher prime.

It is the first member of the first cluster of two square-primes; of the form p2 × q, specifically 22 × 11 = 44 and 32 × 5 = 45. The next such cluster of two square-primes comprises 22 × 29 = 116, and 32 × 13 = 117.

44 has an aliquot sum of 40, within an aliquot sequence of three composite numbers (44, 40, 50, 43, 1, 0) rooted in the prime 43-aliquot tree.

Since the greatest prime factor of 442 + 1 = 1937 is 149 and thus more than 44 twice, 44 is a Størmer number.[3] Given Euler's totient function, φ(44) = 20 and φ(69) = 44.

44 is a tribonacci number, preceded by 7, 13, and 24, whose sum it equals.[4]

44 is the number of derangements of 5 items.[5]

There are only 44 kinds of Schwarz triangles, aside from the infinite dihedral family of triangles (p 2 2) with p = {2, 3, 4, ...}.[6]

There are 44 distinct stellations of the truncated cube and truncated octahedron, per Miller's rules.[7]

44 four-dimensional crystallographic point groups of a total 227 contain dual enantiomorphs, or mirror images.[8]

There are forty-four classes of finite simple groups that arise from four general families of such groups:

Sometimes the Tits group is considered a 17th non-strict simple group of Lie type, or a 27th sporadic group, which would yield a total of 45 finite simple groups.

In science

Astronomy

In technology

In other fields

Forty-four is:

  • The total number of candles lit on the menorah during the Jewish holiday of Chanukah, which starts on the 25th day of the Hebrew month of Kislev and ends on the 2nd or the 3rd day of Tevet.
  • The number of candles in a box of Hanukkah candles.
  • The name of a mysterious savior of Poland prophesied by the Polish national poet Adam Mickiewicz in his masterpiece dramatic poem Dziady (Forefathers): In scene 5 of act 3, the priest Piotr announces a "reviver of the nation" who is to bring back the lost freedom of Poland, and describes him with these words:
Born from a foreign mother, his blood of ancient heroes,
And his name will be forty and four.

Historical years

AD 44, 44 BC, 1944, etc.

See also

References

  1. ^ "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  3. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  4. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  5. ^ "Sloane's A000166 : Subfactorial or rencontres numbers, or derangements". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  6. ^ Messer, Peter W. (2002). "Closed-Form Expressions for Uniform Polyhedra and Their Duals" (PDF). Discrete & Computational Geometry. Springer. 27 (3): 353–355, 372–373. doi:10.1007/s00454-001-0078-2. MR 1921559. S2CID 206996937. Zbl 1003.52006.
  7. ^ Webb, Robert. "Enumeration of Stellations". www.software3d.com. Archived from the original on 2022-11-26. Retrieved 2022-11-25.
  8. ^ Souvignier, Bernd (2003). "Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6". Acta Crystallographica Section A. 59 (3): 217. doi:10.1107/s0108767303004161. PMID 12714771. S2CID 26198482. Zbl 1370.20045.
  9. ^ "Vicks Formula 44 oral: Uses, Side Effects, Interactions, Pictures, Warnings & Dosing - WebMD". www.webmd.com. Retrieved 2021-04-11.
  10. ^ "The 15 Best Megadeth Songs: Critic's Picks". Billboard. Retrieved 2021-04-11.
  11. ^ "O martírio do preso número 44". Jornal Observador (in Portuguese). Retrieved 2017-01-15.
  12. ^ "José Sócrates é o recluso 44". Jornal Expresso (in European Portuguese). Retrieved 2021-04-11.
This page was last edited on 19 February 2024, at 19:49
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