27 (twenty-seven) is the natural number following 26 and preceding 28.

← 26 27 28 →
Cardinaltwenty-seven
Ordinal27th
Factorization33
Divisors1, 3, 9, 27
Greek numeralΚΖ´
Roman numeralXXVII
Binary110112
Ternary10003
Senary436
Octal338
Duodecimal2312
Hexadecimal1B16

Mathematics

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Including the null-motif, there are 27 distinct hypergraph motifs.[1]

 
The Clebsch surface, with 27 straight lines

There are exactly twenty-seven straight lines on a smooth cubic surface,[2] which give a basis of the fundamental representation of Lie algebra  .[3][4]

The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint 3 by 3 matrices of quaternions, is 27-dimensional;[5] its automorphism group is the 52-dimensional exceptional Lie algebra  [6]

There are twenty-seven sporadic groups, if the non-strict group of Lie type   (with an irreducible representation that is twice that of   in 104 dimensions)[7] is included.[8]

In Robin's theorem for the Riemann hypothesis, twenty-seven integers fail to hold   for values   where   is the Euler–Mascheroni constant; this hypothesis is true if and only if this inequality holds for every larger  [9][10][11]

The Clebsch surface has 27 exceptional lines can be defined over the real numbers.

In science

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Astronomy

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Electronics

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In language and literature

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In astrology

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  • 27 Nakṣatra or lunar mansions in Hindu astrology.

In music

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  • "27", the name of a song by Biffy Clyro on their 2002 debut album, Blackened Sky
  • "27", the name of a song by Title Fight on their 2011 album, Shed

In sports

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  • The value of all the colors in snooker add up to 27.
  • The number of outs in a regulation baseball game for each team at all adult levels, including professional play, is 27.
  • The New York Yankees have won 27 World Series championships, the most of any team in the MLB.

In other fields

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Twenty-seven is also:

  • A-27, American attack aircraft.
  • The code for international direct-dial phone calls to South Africa.
  • The name of a cigarette, Marlboro Blend No. 27.
  • The number of the French department Eure.
  • The number of the Chiefs and Elders in the Maghan Gbara, the traditional authority of a tribal confederation in Ghana.
  • The current number of countries in the European Union, as of 2024.

See also

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Notes

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References

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  1. ^ Lee, Geon; Ko, Jihoon; Shin, Kijung (2020). "Hypergraph Motifs: Concepts, Algorithms, and Discoveries". In Balazinska, Magdalena; Zhou, Xiaofang (eds.). 46th International Conference on Very Large Data Bases. Proceedings of the VLDB Endowment. Vol. 13. ACM Digital Library. pp. 2256–2269. arXiv:2003.01853. doi:10.14778/3407790.3407823. ISBN 9781713816126. OCLC 1246551346. S2CID 221779386.
  2. ^ Baez, John Carlos (February 15, 2016). "27 Lines on a Cubic Surface". AMS Blogs. American Mathematical Society. Retrieved October 31, 2023.
  3. ^ Aschbacher, Michael (1987). "The 27-dimensional module for E6. I". Inventiones Mathematicae. 89. Heidelberg, DE: Springer: 166–172. Bibcode:1987InMat..89..159A. doi:10.1007/BF01404676. MR 0892190. S2CID 121262085. Zbl 0629.20018.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A121737 (Dimensions of the irreducible representations of the simple Lie algebra of type E6 over the complex numbers, listed in increasing order.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved October 31, 2023.
  5. ^ Kac, Victor Grigorievich (1977). "Classification of Simple Z-Graded Lie Superalgebras and Simple Jordan Superalgebras". Communications in Algebra. 5 (13). Taylor & Francis: 1380. doi:10.1080/00927877708822224. MR 0498755. S2CID 122274196. Zbl 0367.17007.
  6. ^ Baez, John Carlos (2002). "The Octonions". Bulletin of the American Mathematical Society. 39 (2). Providence, RI: American Mathematical Society: 189–191. doi:10.1090/S0273-0979-01-00934-X. MR 1886087. S2CID 586512. Zbl 1026.17001.
  7. ^ Lubeck, Frank (2001). "Smallest degrees of representations of exceptional groups of Lie type". Communications in Algebra. 29 (5). Philadelphia, PA: Taylor & Francis: 2151. doi:10.1081/AGB-100002175. MR 1837968. S2CID 122060727. Zbl 1004.20003.
  8. ^ Hartley, Michael I.; Hulpke, Alexander (2010). "Polytopes Derived from Sporadic Simple Groups". Contributions to Discrete Mathematics. 5 (2). Alberta, CA: University of Calgary Department of Mathematics and Statistics: 27. doi:10.11575/cdm.v5i2.61945. ISSN 1715-0868. MR 2791293. S2CID 40845205. Zbl 1320.51021.
  9. ^ Axler, Christian (2023). "On Robin's inequality". The Ramanujan Journal. 61 (3). Heidelberg, GE: Springer: 909–919. arXiv:2110.13478. Bibcode:2021arXiv211013478A. doi:10.1007/s11139-022-00683-0. S2CID 239885788. Zbl 1532.11010.
  10. ^ Robin, Guy (1984). "Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann" (PDF). Journal de Mathématiques Pures et Appliquées. Neuvième Série (in French). 63 (2): 187–213. ISSN 0021-7824. MR 0774171. Zbl 0516.10036.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A067698 (Positive integers such that sigma(n) is greater than or equal to exp(gamma) * n * log(log(n)).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved October 31, 2023.
  12. ^ "Dark Energy, Dark Matter | Science Mission Directorate". science.nasa.gov. Retrieved November 8, 2020.
  13. ^ Steve Jenkins, Bones (2010), ISBN 978-0-545-04651-0
  14. ^ "Catalog of Solar Eclipses of Saros 27". NASA Eclipse Website. NASA. Retrieved February 27, 2022.
  15. ^ "Catalog of Lunar Eclipses in Saros 27". NASA Eclipse Website. NASA. Retrieved February 27, 2022.
  16. ^ "SpanishDict Grammar Guide". SpanishDict. Retrieved August 19, 2020.

Further reading

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Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987), p. 106.

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