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
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 September 18, 2024

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.

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

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 $\mathrm {M} _{11}$ 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

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

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 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.

In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 3². The smallest positive square-free numbers are

In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial with integer coefficients. The best-known transcendental numbers are $π$ and $e$ . The quality of a number being transcendental is called transcendence.

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry.

<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.

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.

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

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.

104 is the natural number following 103 and preceding 105.

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

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.

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.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[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.

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[1]