27 (number)

Template:Use mdy datesTemplate:Infobox number 27 (twenty-seven) is the natural number following 26 and preceding 28.

Mathematics

Including the null-motif, there are 27 distinct hypergraph motifs.<ref>Template:Cite book</ref>

File:Clebsch diagonal cubic surface.png

The Clebsch surface, with 27 straight lines

There are exactly twenty-seven straight lines on a smooth cubic surface,<ref>Template:Cite web</ref> which give a basis of the fundamental representation of Lie algebra <math>\mathrm {E_{6}}</math>.<ref>Template:Cite journal</ref><ref>Template:Cite OEIS</ref>

The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint 3 by 3 matrices of quaternions, is 27-dimensional;<ref>Template:Cite journal</ref> its automorphism group is the 52-dimensional exceptional Lie algebra <math>\mathrm {F_{4}}.</math><ref>Template:Cite journal</ref>

There are twenty-seven sporadic groups, if the non-strict group of Lie type <math>\mathrm {T}</math> (with an irreducible representation that is twice that of <math>\mathrm {F_{4}}</math> in 104 dimensions)<ref>Template:Cite journal</ref> is included.<ref>Template:Cite journal</ref>

In Robin's theorem for the Riemann hypothesis, twenty-seven integers fail to hold <math>\sigma(n) < e^\gamma n \log \log n </math> for values <math>n \leq 5040,</math> where <math>\gamma</math> is the Euler–Mascheroni constant; this hypothesis is true if and only if this inequality holds for every larger <math>n.</math><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite OEIS</ref>

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

It is possible to arrange 27 vertices and connect them with edges to create the Holt graph.

27 is 3³, and therefore, it is the second tetration of 3 (²3).

In other fields

• The 27 club refers to the age when many popular music figures died.
• The ASCII escape character is encoded as <syntaxhighlight lang="text" class="" style="" inline="1">27</syntaxhighlight>.

See also

• 72 (number) – 27 reversed
• Cube (algebra)
• Template:Sectionlink for his frequent use of the number

References

Further reading

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

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