11 (number)

For other uses, see 11.

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

← 10 11 12 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
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.

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.^{[citation needed]} 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)

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.^[8]

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.^{[citation needed]}

List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	25	50	100	1000
11 × x	11	22	33	44	55	66	77	88	99	110	121	132	143	154	165	176	187	198	209	220	275	550	1100	11000

Division	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
11 ÷ x	11	5.5	3.6	2.75	2.2	1.83	1.571428	1.375	1.2	1.1	1	0.916	0.846153	0.7857142	0.73
x ÷ 11	0.09	0.18	0.27	0.36	0.45	0.54	0.63	0.72	0.81	0.90	1	1.09	1.18	1.27	1.36

Exponentiation	1	2	3	4	5	6	7	8	9	10	11
11x	11	121	1331	14641	161051	1771561	19487171	214358881	2357947691	25937424601	285311670611
x11	1	2048	177147	4194304	48828125	362797056	1977326743	8589934592	31381059609	100000000000	285311670611

Music

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.

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.

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.

Mysticism

The number 11 (alongside its multiples 22 and 33) are master numbers in numerology, especially in New Age.^[9]

References

1. Bede, Eccl. Hist., Bk. V, Ch. xviii.
2. Specifically, in the line jjvjv ðæt rice hæfde endleofan wintra.^[1]
3. 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.). "Sequence A001359 (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.

External links

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