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.

The Clebsch surface, with 27 straight lines

There are exactly twenty-seven straight lines on a smooth cubic surface, which give a basis of the fundamental representation of Lie algebra ${\mathrm{E}}_{\mathrm{6}}$.

The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint 3 by 3 matrices of quaternions, is 27-dimensional; its automorphism group is the 52-dimensional exceptional Lie algebra ${\mathrm{F}}_{\mathrm{4}}.$

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 ${\mathrm{F}}_{\mathrm{4}}$ in 104 dimensions) is included.

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

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.

In other fields

• The 27 club refers to the age when many popular music figures died. It connects the age 27 with connotations of an early end.Template:Citation needed

See also

• 72 (number) – 27 reversed

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