|Factorization||22 × 3|
|Divisors||1, 2, 3, 4, 6, 12|
|φ(12) = 4||τ(12) = 6|
|σ(12) = 28||π(12) = 5|
|μ(12) = 0||M(12) = -2|
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.
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.
It derives from the Old English twelf and tuelf, first attested in the 10th-century Lindisfarne Gospels' Book of John.[note 1] It has cognates in every Germanic language (e.g. German zwölf), whose Proto-Germanic ancestor has been reconstructed as *twaliƀi..., from *twa ("two") 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 (analogous to "-teen"). 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" (from the Latin word) 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 ("to leave"), 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 (but in Spanish and Portuguese, 16, and in French, 17 is the first compound number),[dubious ] Japanese 十二 jūni.[clarification needed]
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 (sixteen, twenty-seven, fifteen thousand, but 372 or 15,001). In German orthography, there used to be the widely followed (but unofficial) rule of spelling out numbers up to twelve (zwölf). The Duden[year needed] (the German standard dictionary) mentions this rule as outdated.
Twelve is the smallest abundant number, since it is the smallest integer for which the sum of its proper divisors (1 + 2 + 3 + 4 + 6 = 16) 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 (all of them but with 4 excluded), 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 (the Kepler conjecture). 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(q) whose Fourier coefficients are given by the Ramanujan τ-function and which is (up to a constant multiplier) 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(−1) = −1/, the fact that the abelianization of SL(2,Z) has twelve elements, and even the properties of lattice polygons.
There are 12 Latin squares of size 3 × 3.
|12 × x||12||24||36||48||60||72||84||96||108||120||132||144||156||168||180||192||204||216||228||240||252||264||276||288||300||600||1200||12000|
|12 ÷ x||12||6||4||3||2.4||2||1.714285||1.5||1.3||1.2||1.09||1||0.923076||0.857142||0.8||0.75|
|x ÷ 12||0.083||0.16||0.25||0.3||0.416||0.5||0.583||0.6||0.75||0.83||0.916||1||1.083||1.16||1.25||1.3|
Notably, twelve is the number of full lunations in a solar year, and the number of years for a full cycle of Jupiter (the brightest of the ancient "wandering stars"), hence the number of months in a solar calendar, as well as the number of signs in the Western and the Chinese zodiac.
Ishmael - the first-born son of Abraham - has 12 sons/princes (Genesis 25:16), 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 (Acts) 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. 12:1 mentions a woman—interpreted as the people of Israel, the Church and the Virgin Mary—wearing a crown of twelve stars (representing each of the twelve tribes of Israel). Furthermore, there are 12,000 people sealed from each of the twelve tribes of Israel, making a total of 144,000 (which is the square of 12 multiplied by a thousand).
In English Common Law, the tradition of twelve jurors harks back to the 10th-century law code introduced by Aethelred the Unready.
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.
|१२||Indian and Nepali (Devanāgarī)||十二||Chinese and Japanese|
|௧௨||Tamil||Ⅻ||Roman and Etruscan|
Movies with the number twelve or its variations in their titles include: