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12 (twelve) 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[edit]

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.^[1][2][3] 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.^{[note 1][5]} 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.^[5] It is sometimes compared with the Lithuaniandvýlika, although -lika is used as the suffix for all numbers from 11 to 19 (analogous to "-teen").^[5] Every other Indo-European language instead uses a form of "two"+"ten", such as the Latinduōdecim.^[5] 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,^[6] 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.^[5] The Lithuanian suffix is also considered to share a similar development.^[5] The suffix *-lif- has also been connected with reconstructions of the Proto-Germanic for ten.^[6][7]

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 – discuss]} Japanese 十二 jūni.^{[clarification needed]}

Written representation[edit]

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).^[8] 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.

Mathematical properties[edit]

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.^[9]

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.^[10] 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.^[11]

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-facedpolyhedron 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 latticesphere 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 Ramanujanτ-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) = −1/12, the fact that the abelianization of SL(2,Z) 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 (12₁₀ [twelve] = 10₁₂), 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 (such as hexadecimal), twelve is represented as C. In base 10, the number 12 is a Harshad number.

List of basic calculations[edit]

In nature[edit]

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 Chinesezodiac.

Religion[edit]

The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.^[12]

Ancient Greek religion[edit]

Judaism[edit]

• The significance is especially pronounced in the Hebrew Bible.

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.^[14] 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.

Hinduism[edit]

• There are twelve Jyotirlinga(Self-formed Lingas) of Lord Shiva in Hindu temples across India according to the Shaiva tradition.
• The Sun god Surya has 12 names.
• The Monkey god Hanuman has 12 names.
• There are 12 Petals in Anahata or "heart chakra".
• There are frequently said to be 12 Âdityas.

Others[edit]

In the King Arthur Legend, Arthur is said to subdue 12 rebel princes and to win 12 great battles against Saxon invaders.^[15]

In TwelverShi'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[edit]

• The lunar year is 12 lunar months. Adding 11 or 12 days completes the solar year.^[16]
• Most calendar systems - solar or lunar - have twelve months in a year.
• The Chinese use a 12-year cycle for time-reckoning called Earthly Branches.
• There are twelve hours in a half day, numbered one to twelve for both the ante meridiem (a.m.) and the post meridiem (p.m.). 12:00 p.m. is midday or noon, and 12:00 a.m. is midnight.
• The basic units of time (60 seconds, 60 minutes, 24 hours) are evenly divisible by twelve into smaller units.

In numeral systems[edit]

In science[edit]

In sports[edit]

• In both soccer and American football, the number 12 can be a symbolic reference to the fans because of the support they give to the 11 players on the field. Texas A&M University reserves the number 12 jersey for a walk-on player who represents the original "12th Man", a fan who was asked to play when the team's reserves were low in a college American football game in 1922. Similarly, Bayern Munich, Hammarby, Feyenoord, Atlético Mineiro, Flamengo, Seattle Seahawks, Portsmouth and Cork City do not allow field players to wear the number 12 on their jersey because it is reserved for their supporters.
• In Canadian football, 12 is the maximum number of players that can be on the field of play for each team at any time.
• In cricket, another sport with eleven players per team, teams may select a "12th man", who may replace an injured player for the purpose of fielding (but not batting or bowling).
• In women's lacrosse, each team has 12 players on the field at any given time, except in penalty situations.
• In rugby league, one of the starting second-row forwards wears the number 12 jersey in most competitions. An exception is in the Super League, which uses static squad numbering.
• In rugby union, one of the starting centres, most often but not always the inside centre, wears the 12 shirt.
• In an NBA game, a quarter lasts 12 minutes.

In technology[edit]

In the arts[edit]

Film[edit]

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

Television[edit]

Theatre[edit]

Literature[edit]

Music[edit]

Music theory[edit]

Pop music[edit]

Art theory[edit]

• There are twelve basic hues in the color wheel; 3 primary colors (red, yellow, blue), 3 secondary colors (orange, green & purple) and 6 tertiary colors (names for these vary, but are intermediates between the primaries and secondaries).

Games[edit]

In other fields[edit]

• There are 12 troy ounces in a troy pound (used for precious metals).
• In the former British currency system, there were twelve pence in a shilling.
• In Greek mythology, the number of Labours of Heracles was increased from ten to make twelve.
• In English, twelve is the number of greatest magnitude that has just one syllable.
• There are normally twelve pairs of ribs in the human body.
• The Twelve Tables or Lex Duodecim Tabularum, more informally simply Duodecim Tabulae was the ancient legislation underlying Roman law.
• In the United States, twelve people are appointed to sit on a jury for felony trials in all but four states, and in federal and Washington, D.C. courts. The number of jurors gave the title to the play (and subsequent films) Twelve Angry Men.
• Twelve people have walked on Earth's moon.
• The United States is divided into twelve Federal Reserve Districts (Boston, New York, Philadelphia, Cleveland, Richmond, Atlanta, Chicago, St. Louis, Minneapolis, Kansas City, Dallas, and San Francisco); American paper currency has serial numbers beginning with one of twelve different letters, A through L, representing the Federal Reserve Bank from which the currency originated.
• According to UFO conspiracy theory, Majestic 12 is a secret committee, allegedly set up by U.S. President Harry S. Truman to investigate the Roswell UFO incident and cover up future extraterrestrial contact.
• 12 is the number of the French department Aveyron.
• King Arthur's round table had 12 knights plus King Arthur himself.
• 12 inches in a foot.
• Alcoholics Anonymous has 12 steps, 12 traditions and 12 concepts for world service.
• Wilhelm Heinrich Schüßler developed a list of 12 biochemical cell salts, also known as tissue salts.

See also[edit]

Notes[edit]

References[edit]

Citations[edit]

Sources[edit]

Journal articles

External links[edit]