11 (number)

Mathematics

11 is a prime number, and a super-prime. 11 forms a twin prime pair with 13, and sexy prime pairs with both 5 and 17. 11 is also the first prime exponent that does not yield a Mersenne prime because 2¹¹ − 1 is not prime:

2¹¹ − 1 = 2047 = 23 × 89.

(5, 11) is a pair of brown numbers because 5! + 1 = 11². Only three such pairs of numbers are known. Rows in Pascal's triangle can be seen as representation of powers of 11.

Geometry

An 11-sided polygon is called a hendecagon, or undecagon. A regular hendecagon is the polygon with the fewest number of sides that is not able to be constructed with a straightedge, compass, and angle trisector.

The Mathieu group ${\displaystyle {\mathrm{M}}_{11}}$ is the smallest of twenty-six sporadic groups. It has order ${\displaystyle 7920=2^4\cdot 3^2\cdot 5\cdot 11=8\cdot 9\cdot 10\cdot 11}$, with 11 as its largest prime factor. ${\displaystyle {\mathrm{M}}_{11}}$ is the maximal subgroup Mathieu group ${\displaystyle {\mathrm{M}}_{12}}$, where 11 is also its largest prime factor.

List of basic calculations

Music

The interval of an octave plus a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale.

In just intonation and microtonal music theory, the number 11 or the ratio 11/8 denotes an interval between that of a perfect fifth and of a tritone; eleven eighths the frequency of the fundamental tone, or the eleventh harmonic. It is an unstable interval and appears mostly in contemporary and experimental music.

Cultural references

Film

In the mockumentary film "This Is Spinal Tap", the idiomatic phrase up to eleven is coined to allude to going beyond typical limits, in this case guitar amplifier volume levels.

"Eleventh hour"

Being one hour before 12:00, the eleventh hour means the last possible moment to take care of something, and often implies a situation of urgent danger or emergency (see Doomsday clock). "The eleventh hour" is a phrase in the Parable of the Workers in the Vineyard in the Bible.

Eleventh Night

In Protestant communities in Northern Ireland, bonfires are lit to mark the eve of Protestant William III of England's victory over the Catholic James II of England at the Battle of the Boyne.

Languages

While 11 has its own name in Germanic languages such as English, German, or Swedish, and some Latin-based languages such as Spanish, Portuguese, and French, it is the first compound number in many other languages: Chinese 十一 shí yī, Korean 열하나 yeol hana or 십일 ship il.

In Basque, hamaika, "11", also means "a lot".

Religion

The number 11 (alongside its multiples 22 and 33) are master numbers in numerology, especially in New Age.