11 (number)

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11 (eleven) is the natural number following 10 and preceding 12. It is the smallest number whose name has three syllables.

Contents

10 11 12
Cardinal eleven
Ordinal 11th
(eleventh)
Numeral system undecimal
Factorization prime
Prime 5th
Divisors 1, 11
Greek numeral ΙΑ´
Roman numeral XI, xi
Greek prefix hendeca-/hendeka-
Latin prefix undeca-
Binary 10112
Ternary 1023
Senary 156
Octal 138
Duodecimal B12
Hexadecimal B16
Bangla ১১
Hebrew numeral י"א
Devanagari numerals ११
Malayalam ൰൧
Tamil numerals கக
Telugu ౧౧
Babylonian numeral 𒌋𒐕

Name

"Eleven" derives from the Old English ęndleofon, which is first attested in Bede's late 9th-century Ecclesiastical History of the English People . [2] [3] It has cognates in every Germanic language (for example, German elf), whose Proto-Germanic ancestor has been reconstructed as *ainalifa-, [4] from the prefix *aina- (adjectival "one") and suffix *-lifa-, of uncertain meaning. [3] It is sometimes compared with the Lithuanian vienúolika, though -lika is used as the suffix for all numbers from 11 to 19. [3]

The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as *ainlifun. This was formerly thought to be derived from Proto-Germanic *tehun ("ten"); [3] [5] it is now sometimes connected with *leikʷ- or *leip- ("left; remaining"), with the implicit meaning that "one is left" after counting to ten. [3]

Mathematics

11 is a prime number, and a super-prime. 11 forms a twin prime with 13, [6] 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. [7] Rows in Pascal's triangle can be seen as representation of powers of 11. [8]

Geometry

Copper engraving of a hendecagon, by Anton Ernst Burkhard von Birckenstein (1698) Fotothek df tg 0004812 Geometrie ^ Architektur ^ Festungsbau ^ Vermessung.jpg
Copper engraving of a hendecagon, 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. [9]

The Mathieu group is the smallest of twenty-six sporadic groups. It has order , with 11 as its largest prime factor. is the maximal subgroup Mathieu group , where 11 is also its largest prime factor.[ citation needed ]

List of basic calculations

Multiplication 123456789101112131415161718192025501001000
11 × x11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 275 550 1100 11000
Division 123456789101112131415
11 ÷ x115.53.62.752.21.831.5714281.3751.21.110.9160.8461530.78571420.73
x ÷ 110.090.180.270.360.450.540.630.720.810.90 1 1.091.181.271.36
Exponentiation 1234567891011
11x11121133114641161051177156119487171214358881235794769125937424601285311670611
x11120481771474194304488281253627970561977326743858993459231381059609100000000000285311670611

Music

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

Cultural references

Film

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.

"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 열하나yeol hana or 십일ship il.

Mysticism

The number 11 (alongside its multiples 22 and 33) are master numbers in numerology, especially in New Age. [10]

Religion

The Quran refers to the number eleven in Surah Yusuf, verse 4: [11]

˹Remember˺ when Joseph said to his father, “O my dear father! Indeed I dreamt of eleven stars, and the sun, and the moon—I saw them prostrating to me!”

The dream came true at the end of the story when Yusuf's eleven brothers and parents prostrated before him in Egypt. [12]

In the Bible, Joseph has 11 brothers.

References

  1. Bede, Eccl. Hist. , Bk. V, Ch. xviii.
  2. Specifically, in the line Osred ðæt rice hæfde endleofan wintra. [1]
  3. 1 2 3 4 5 Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
  4. Kroonen, Guus (2013). Etymological Dictionary of Proto-Germanic. Leiden: Brill. p. 11f. ISBN   978-90-04-18340-7.
  5. Dantzig, Tobias (1930), Number: The Language of Science.
  6. Sloane, N. J. A. (ed.). "SequenceA001359(Lesser of twin primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-01-22.
  7. Weisstein, Eric W. "Brocard's Problem". MathWorld . Retrieved 24 July 2025.
  8. Mueller, Francis J. (1965). "More on Pascal's Triangle and powers of 11". The Mathematics Teacher. 58 (5): 425–428. doi:10.5951/MT.58.5.0425. JSTOR   27957164.
  9. Gleason, Andrew M. (1988). "Angle trisection, the heptagon, and the triskaidecagon" . American Mathematical Monthly . 95 (3). Taylor & Francis, Ltd: 191–194. doi:10.2307/2323624. JSTOR   2323624. MR   0935432. S2CID   119831032.
  10. Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN   978-1-57324-560-9.
  11. "Surah Yusuf - 4". Quran.com. Retrieved 2025-06-23.
  12. "Surah Yusuf - 100". Quran.com. Retrieved 2025-06-23.

Grimes, James. "Eleven". Numberphile. Brady Haran. Archived from the original on 2017-10-15. Retrieved 2016-01-03.