12 (number)




φ = 4τ = 6
σ = 28π = 5
μ = 0M = -2

12 is the natural number following 11 and preceding 13. The product of the first 3 factorials, twelve is a superior highly composite number, divisible by 2, 3, 4, and 6.
It is approximately the number of full lunations of the moon in a year, and the number of years for a full cycle of Jupiter, which was historically considered the brightest "wandering star". It is central to many systems of timekeeping, including the Western calendar and units of time of day, and frequently appears in the world's major religions.

Name

Twelve is the largest number with a single-syllable name in English. Early Germanic numbers have been theorized to have been non-decimal: evidence includes the unusual phrasing of eleven and twelve, the former use of "hundred" to refer to groups of 120, and the presence of glosses such as "tentywise" or "ten-count" in medieval texts showing that writers could not presume their readers would normally understand them that way. Such uses gradually disappeared with the introduction of Arabic numerals during the 12th-century Renaissance.
Derived from Old English, twelf and tuelf are first attested in the 10th-century Lindisfarne Gospels' Book of John. It has cognates in every Germanic language, whose Proto-Germanic ancestor has been reconstructed as twaliƀi..., from twa and suffix -lif- or -liƀ- of uncertain meaning. It is sometimes compared with the Lithuanian dvýlika, although -lika is used as the suffix for all numbers from 11 to 19. Every other Indo-European language instead uses a form of "two"+"ten", such as the Latin duōdecim. The usual ordinal form is "twelfth" but "dozenth" or "duodecimal" is also used in some contexts, particularly base-12 numeration. Similarly, a group of twelve things is usually a "dozen" but may also be referred to as a "dodecad" or "duodecad". The adjective referring to a group of twelve is "duodecuple".
As with eleven, the earliest forms of twelve are often considered to be connected with Proto-Germanic liƀan or liƀan, with the implicit meaning that "two is left" after having already counted to ten. The Lithuanian suffix is also considered to share a similar development. The suffix -lif- has also been connected with reconstructions of the Proto-Germanic for ten.
While, as mentioned above, 12 has its own name in Germanic languages such as English, German, and Swedish, it is a compound number in many other languages, e.g. Italian dodici, Japanese 十二 jūni.

Written representation

In prose writing, twelve, being the last single-syllable numeral, is sometimes taken as the last number to be written as a word, and 13 the first to be written using digits.
This is not a binding rule, and in English language tradition, it is sometimes recommended to spell out numbers up to and including either nine, ten or twelve, or even ninety-nine or one hundred. Another system spells out all numbers written in one or two words.
In German orthography, there used to be the widely followed rule of spelling out numbers up to twelve . The Duden mentions this rule as outdated.

Mathematical properties

Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12. Twelve is also a highly composite number, the next one being twenty-four.
Twelve is the smallest abundant number, since it is the smallest integer for which the sum of its proper divisors is greater than itself. Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there is a subset of 12's proper divisors that add up to 12, 12 is a semiperfect number.
If an odd perfect number is of the form 12k + 1, it has at least twelve distinct prime factors.
A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres . Twelve is also the kissing number in three dimensions.
Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant Δ whose Fourier coefficients are given by the Ramanujan -function and which is the 24th power of the Dedekind eta function. This fact is related to a constellation of interesting appearances of the number twelve in mathematics ranging from the value of the Riemann zeta function at −1 i.e. ζ = −, the fact that the abelianization of SL has twelve elements, and even the properties of lattice polygons.
There are twelve Jacobian elliptic functions and twelve cubic distance-transitive graphs.
There are 12 Latin squares of size 3 × 3.
The duodecimal system, which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia.
In base thirteen and higher bases, twelve is represented as C. In base 10, the number 12 is a Harshad number.

List of basic calculations

Multiplication12345678910111213141516171819202122232425501001000
12 × x1224364860728496108120132144156168180192204216228240252264276288300600120012000

Division12345678910111213141516
12 ÷ x126432.421.1.51.1.21.10.0.0.80.75
x'' ÷ 120.080.10.250.0.410.50.580.0.750.80.9111.081.11.251.

Exponentiation12345678910111213
12121441728207362488322985984358318084299816965159780352619173642247430083706888916100448256106993205379072
x14096531441167772162441406252176782336138412872016871947673628242953648110000000000003138428376721891610044825623298085122481

In nature

Notably, twelve is the number of full lunations in a solar year, and the number of years for a full cycle of Jupiter, hence the number of months in a solar calendar, as well as the number of signs in the Western and the Chinese zodiac.

Religion

The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.

Ancient Greek religion

Ishmael - the first-born son of Abraham - has 12 sons/princes, and Jacob also has 12 sons, who are the progenitors of the Twelve Tribes of Israel. This is reflected in Christian tradition, notably in the twelve Apostles. When Judas Iscariot is disgraced, a meeting is held to add Saint Matthias to complete the number twelve once more.
The Book of Revelation contains much numerical symbolism, and many of the numbers mentioned have 12 as a divisor. mentions a woman—interpreted as the people of Israel, the Church and the Virgin Mary—wearing a crown of twelve stars. Furthermore, there are 12,000 people sealed from each of the twelve tribes of Israel, making a total of 144,000.
In English Common Law, the tradition of twelve jurors harks back to the 10th-century law code introduced by Aethelred the Unready.

Hinduism

In the King Arthur Legend, Arthur is said to subdue 12 rebel princes and to win 12 great battles against Saxon invaders.
In Twelver Shi'a Islam, there are twelve Imams, legitimate successors of the Islamic prophet, Muhammad. These twelve early leaders of Islam are—Ali, Hasan, Husayn, and nine of Husayn's descendants.
Sura 12 in the Quran is sura Yusuf, narrating the story of the sons of Jacob.

Timekeeping

۱۲Arabic១២KhmerԺԲArmenian
১২BanglaΔΙΙAttic Greek--
יבHebrewV20-Z1-Z1Egyptian--
१२Indian and Nepali 十二Chinese and Japanese--
௧௨TamilXIIRoman and Etruscan--
๑๒ThaiIIXChuvash--
౧౨Telugu١٢Urdu--
ιβʹIonian Greek൧൨Malayalam--

In science

Film

Movies with the number twelve or its variations in their titles include:

Music theory