11 (number)

Last updated
10 11 12
Cardinal eleven
Ordinal 11th
(eleventh)
Numeral system undecimal
Factorization prime
Prime 5th
Divisors 1, 11
Greek numeral ΙΑ´
Roman numeral 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

11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.

Contents

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 (analogously to "-teen"). [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.

The first prime exponent that does not yield a Mersenne prime is 11.

11 is part of a pair of Brown numbers. Only three such pairs of numbers are known. Rows in Pascal's triangle can be seen as representation of powers of 11. [7]

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 first polygon that is not able to be constructed with the aid of an angle trisector. [8]

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 550110011000
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

Science

In chemistry, Group 11 of the Periodic Table of the Elements (IUPAC numbering) consists of the three coinage metals copper, silver, and gold known from antiquity, and roentgenium, a recently synthesized superheavy element. 11 is the number of spacetime dimensions in M-theory.

In astronomy

Apollo 11 was the first crewed spacecraft to land on the Moon. In our solar system, the Sun has a sunspot cycle's periodicity that is approximately 11 years.

Music

The interval of an octave plus a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale. Regarding musical instruments, there are 11 thumb keys on a bassoon, not counting the whisper key. (A few bassoons have a 12th thumb key.)

Sports and games

In sports, there are 11 players on an association football (soccer) team, 11 players on an American football team during play, 11 players on a cricket team on the field, and 11 players in a field hockey team. In the game of blackjack, an ace can count as either one or 11, whichever is more advantageous for the player.

Cultural references

The idiom "up to eleven", from the movie This Is Spinal Tap.

In Canada

The stylized maple leaf on the Flag of Canada has 11 points. The CA$ one-dollar loonie is in the shape of an 11-sided hendecagon, and clocks depicted on Canadian currency, like the Canadian 50-dollar bill, show 11:00.

"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.

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. [9]

Related Research Articles

42 (forty-two) is the natural number that follows 41 and precedes 43.

10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

12 (twelve) is the natural number following 11 and preceding 13. Twelve is a superior highly composite number, divisible by the numbers from 1 to 4, and 6.

15 (fifteen) is the natural number following 14 and preceding 16.

20 (twenty) is the natural number following 19 and preceding 21.

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.

90 (ninety) is the natural number following 89 and preceding 91.

22 (twenty-two) is the natural number following 21 and preceding 23.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or six dozen.

32 (thirty-two) is the natural number following 31 and preceding 33.

58 (fifty-eight) is the natural number following 57 and preceding 59.

63 (sixtboo-three) is the natural number following sixtboo and preceding seventboo.

<span class="mw-page-title-main">120 (number)</span> Natural number

120 is the natural number following 119 and preceding 121. It is five sixths of a gross, or ten dozens.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

135 is the natural number following 134 and preceding 136.

181 is the natural number following 180 and preceding 182.

177 is the natural number following 176 and preceding 178.

277 is the natural number following 276 and preceding 278.

14 (fourteen) is the natural number following 13 and preceding 15.

References

  1. Bede, Eccl. Hist. , Bk. V, Ch. xviii.
  2. Specifically, in the line jjvjv 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. 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.
  8. 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.
  9. Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN   978-1-57324-560-9.

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