11 (number)

← 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

Last updated January 09, 2025

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

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

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 $\mathrm {M} _{11}$ is the smallest of twenty-six sporadic groups. It has order $7920=2^{4}\cdot 3^{2}\cdot 5\cdot 11=8\cdot 9\cdot 10\cdot 11$ , with 11 as its largest prime factor. $\mathrm {M} _{11}$ is the maximal subgroup Mathieu group $\mathrm {M} _{12}$ , 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
11^x	11	121	1331	14641	161051	1771561	19487171	214358881	2357947691	25937424601	285311670611
x¹¹	1	2048	177147	4194304	48828125	362797056	1977326743	8589934592	31381059609	100000000000	285311670611

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 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

The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.

In mathematics, a finite field or Galois field is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the integers mod when $is a prime number.$

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

<span class="mw-page-title-main">Prime number</span> Number divisible only by 1 or itself

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

<span class="mw-page-title-main">Angle trisection</span> Construction of an angle equal to one third a given angle

Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass.

12 (twelve) is the natural number following 11 and preceding 13.

3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies.

33 (thirty-three) is the natural number following 32 and preceding 34.

23 (twenty-three) is the natural number following 22 and preceding 24.

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.

63 (sixty-three) is the natural number following 62 and preceding 64.

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

<span class="mw-page-title-main">Constructible polygon</span> Regular polygon that can be constructed with compass and straightedge

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are known.

In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon.

In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product:

In number theory, a Pierpont prime is a prime number of the form $for some nonnegative integers u and v . That is, they are the prime numbers p for which p - 1 is 3-smooth. They are named after the mathematician James Pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. The same characterization applies to polygons that can be constructed using ruler, compass, and angle trisector, or using paper folding.$

5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number.

In mathematical logic, Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature of Skolem arithmetic contains only the multiplication operation and equality, omitting the addition operation entirely.

In geometry, an icositrigon or 23-gon is a 23-sided polygon. The icositrigon has the distinction of being the smallest regular polygon that is not neusis constructible.

References

↑ Bede, Eccl. Hist. , Bk. V, Ch. xviii.
↑ Specifically, in the line jjvjv ðæt rice hæfde endleofan wintra.^[1]
1 2 3 4 5 Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
↑ Kroonen, Guus (2013). Etymological Dictionary of Proto-Germanic. Leiden: Brill. p. 11f. ISBN 978-90-04-18340-7.
↑ Dantzig, Tobias (1930), Number: The Language of Science.
↑ Sloane, N. J. A. (ed.). "SequenceA001359(Lesser of twin primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-01-22.
↑ 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.
↑ 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.
↑ 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.

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[1] Bede, Eccl. Hist. , Bk. V, Ch. xviii.

[2] Specifically, in the line jjvjv ðæt rice hæfde endleofan wintra.^[1]

[oed-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.

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