27 (number)

← 26 27 28 →
← 20 21 22 23 24 25 26 27 28 29 → List of numbers; Integers; ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	twenty-seven
Ordinal	27th
Factorization	33
Divisors	1, 3, 9, 27
Greek numeral	ΚΖ´
Roman numeral	XXVII
Binary	110112
Ternary	10003
Senary	436
Octal	338
Duodecimal	2312
Hexadecimal	1B16

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

Mathematics

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

There are exactly twenty-seven straight lines on a smooth cubic surface,^[2] which give a basis of the fundamental representation of Lie algebra $\mathrm {E_{6}}$ .^[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 $\mathrm {F_{4}} .$ ^[6]

There are twenty-seven sporadic groups, if the non-strict group of Lie type $\mathrm {T}$ (with an irreducible representation that is twice that of $\mathrm {F_{4}}$ in 104 dimensions)^[7] is included.^[8]

In Robin's theorem for the Riemann hypothesis, twenty-seven integers fail to hold $\sigma (n)<e^{\gamma }n\log \log n$ for values $n\leq 5040,$ where $\gamma$ is the Euler–Mascheroni constant; this hypothesis is true if and only if this inequality holds for every larger $n.$ ^[9]^[10]^[11]

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

In science

The Moon revolves around the Earth the same direction as Earth spins but 27 (27.3) times slower.
27km is the circumference of the LHC located at CERN in Meyrin Switzerland
The atomic number of cobalt.
Dark matter is thought to make up 27% of the universe.^[12]
27 is the number of bones in the human hand.^[13]

Astronomy

The Messier object M27, a magnitude 7.5 planetary nebula in the constellation Vulpecula, also known as the Dumbbell Nebula.
The New General Catalogue object NGC 27, a spiral galaxy in the Andromeda constellation.
The Saros number of the solar eclipse series, which began on March 9, 1993, BCE and ended on April 16, 713 BCE.^[14] The duration of Saros series 27 was 1,280.1 years, and it contained 72 solar eclipses. Further, the Saros number of the lunar eclipse series, which began on July 28, 1926 BCE and ended on January 23, 411 BCE.^[15] The duration of Saros series 27 was 1532.5 years, and it contained 86 lunar eclipses.

Electronics

The type 27 vacuum tube (valve), a triode introduced in 1927, was the first tube mass-produced for commercial use to incorporate an indirectly heated cathode. This made it the first vacuum tube that could function as a detector in AC-powered radios. Prior to the introduction of the 27, home radios were powered by a set of three or more storage batteries with voltages of 3 to 135 volts.

In language and literature

The number of letters in the Spanish alphabet.^[16]
The number of books in the New Testament.
The number of generations from David to the Christ according to the Gospel of Matthew. (Mt 1,1-17)
The number of Grievances of the United States Declaration of Independence.
The number of ratified Amendments to the United States Constitution.
Until 1835, the English Alphabet consisted of 27 letters: after "Z" the 27th letter of the alphabet was Ampersand (&)
The total number of letters in the Hebrew alphabet (22 regular letters and 5 final consonants).
Alternate name for The Hunt, a book by William Diehl.
Abbé Faria's prisoner number in the book The Count of Monte Cristo.
In Stephen King's novel It, It returns every 27 years to Derry.
The war led by the Antichrist will begin in the year 1999 and will last 27 years according to Nostradamus.

In astrology

27 Nakṣatra or lunar mansions in Hindu astrology.

In music

"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

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 MLB.

In other fields

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.

Notes

References

^ 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.
^ Baez, John Carlos (February 15, 2016). "27 Lines on a Cubic Surface". AMS Blogs. American Mathematical Society. Retrieved October 31, 2023.
^ 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.
^ 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.
^ 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.
^ 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.
^ 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.
^ 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.
^ 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.
^ 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.
^ 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.
^ "Dark Energy, Dark Matter | Science Mission Directorate". science.nasa.gov. Retrieved November 8, 2020.
^ Steve Jenkins, Bones (2010), ISBN 978-0-545-04651-0
^ "Catalog of Solar Eclipses of Saros 27". NASA Eclipse Website. NASA. Retrieved February 27, 2022.
^ "Catalog of Lunar Eclipses in Saros 27". NASA Eclipse Website. NASA. Retrieved February 27, 2022.
^ "SpanishDict Grammar Guide". SpanishDict. Retrieved August 19, 2020.

External links

Prime Curios! 27 from the Prime Pages
Mystery of the number 27 - Large collection of 27 related trivia and facts.
The 27 Project - collection of sightings of 27 in movies, TV, culture and art

[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.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]