:11 (number)

"Eleven" derives from the Old English {{lang|ang|ęndleofon}}, which is first attested in Bede's late 9th-century Ecclesiastical History of the English People.{{refn|Specifically, in the line {{lang|ang|Osred ðæt rice hæfde endleofan wintra.}}Bede, Eccl. Hist., Bk. V, Ch. xviii.}} It has cognates in every Germanic language (for example, German {{lang|de|elf}}), whose Proto-Germanic ancestor has been reconstructed as {{lang|gem-x-proto|*ainalifa-}},{{cite book|last1=Kroonen|first1=Guus|title=Etymological Dictionary of Proto-Germanic|date=2013| publisher=Brill|location=Leiden|isbn=978-90-04-18340-7|page=11f}} from the prefix {{lang|gem-x-proto|*aina-}} (adjectival "one") and suffix {{lang|gem-x-proto|*-lifa-}}, of uncertain meaning. It is sometimes compared with the Lithuanian {{lang|lt|vienúolika}}, though {{lang|lt|-lika}} is used as the suffix for all numbers from 11 to 19.

The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as {{lang|gem-x-proto|*ainlifun}}. This was formerly thought to be derived from Proto-Germanic {{lang|gem-x-proto|*tehun}} ("ten");{{citation |last=Dantzig |first=Tobias |date=1930 |title=Number: The Language of Science }}. it is now sometimes connected with {{lang|gem-x-proto|*leikʷ-}} or {{lang|gem-x-proto|*leip-}} ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.

11 is a prime number, and a super-prime. 11 forms a twin prime with 13,{{Cite OEIS |A001359 |Lesser of twin primes. |access-date=2023-01-22 }} and sexy pair with 5 and 17. 11 is also the first prime exponent that does not yield a Mersenne prime.

11 is part of a pair of Brown numbers. Only three such pairs of numbers are known.{{Citation needed|date=September 2024}} Rows in Pascal's triangle can be seen as representation of powers of 11.{{cite journal | jstor=27957164 | last1=Mueller | first1=Francis J. | title=More on Pascal's Triangle and powers of 11 | journal=The Mathematics Teacher | year=1965 | volume=58 | issue=5 | pages=425–428 | doi=10.5951/MT.58.5.0425 }}

File:Fotothek df tg 0004812 Geometrie ^ Architektur ^ Festungsbau ^ Vermessung.jpg, by Anton Ernst Burkhard von Birckenstein (1698)]]

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.{{Cite journal|last=Gleason |first=Andrew M. |author-link=Andrew M. Gleason |url=https://www.tandfonline.com/doi/abs/10.1080/00029890.1988.11971989?journalCode=uamm20 |title=Angle trisection, the heptagon, and the triskaidecagon |journal=American Mathematical Monthly |volume= 95 |issue=3 |year= 1988 |publisher=Taylor & Francis, Ltd |pages=191–194 |doi=10.2307/2323624 |mr=935432 |jstor=2323624 |s2cid=119831032 }}

The Mathieu group $\backslash mathrm\{M\}\_\{11\}$ is the smallest of twenty-six sporadic groups. It has order $7920\; =2^\{4\}\backslash cdot3^\{2\}\backslash cdot5\backslash cdot11\; =\; 8\backslash cdot9\backslash cdot10\backslash cdot11$, with 11 as its largest prime factor. $\backslash mathrm\{M\}\_\{11\}$ is the maximal subgroup Mathieu group $\backslash mathrm\{M\}\_\{12\}$, where 11 is also its largest prime factor.{{Citation needed|date=August 2024}}

{{See also|Eleven (disambiguation)#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 the mockumentary film This Is Spinal Tap, the idiomatic phrase up to eleven is coined to allude to going beyond the limitations of a system, in this case music amplifier volume levels.

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.

{{Main Article|Eleventh Night}}

In protestant communities in Northern Ireland bonfires are lit to mark the eve of protestant William III of England victory over the catholic James II of England at the battle of the Boyne

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 {{lang|zh|十一}} {{lang|zh-Latn|shí yī}}, Korean {{lang|ko|열하나}} {{lang|ko-Latn|yeol hana}} or {{lang|ko|십일}} {{lang|ko-Latn|ship il}}.

The number 11 (alongside its multiples 22 and 33) are master numbers in numerology, especially in New Age.{{cite book |last=Sharp |first=Damian |title=Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series) |publisher=Red Wheel |year=2001 |page=7 |language=English |isbn=978-1-57324-560-9 }}

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{{Cite web|last=Grimes|first=James|title=Eleven|url=http://www.numberphile.com/videos/11.html|work=Numberphile|publisher=Brady Haran|access-date=2016-01-03|archive-url=https://web.archive.org/web/20171015073814/http://www.numberphile.com/videos/11.html|archive-date=2017-10-15}}

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