12 (number)

12 (twelve) is the natural number following 11 and preceding 13. The product of the first three factorials, twelve is a superior highly composite number, divisible by 2, 3, 4, and 6. It is central to many systems of counting, including the Western calendar and units of time, and frequently appears in the Abrahamic 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.^[1][2][3] 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.^{[n 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 Lithuanian dvýlika, 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 Latin duōdecim.^[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 "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), Japanese 十二 jūni.

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.^[8]

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.^[9] 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.^[10]

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) = −1/12, 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.

Symbolism

The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.^[11] Notably, twelve is the number of full lunations in a solar year, and hence the number of months in a solar calendar, as well as the number of signs in the Western and the Chinese zodiac.

In Ancient Greek religion, the Twelve Olympians are the principal gods of the pantheon, and Hercules carries out twelve labours.^[12] Several sets of twelve cities are identified in history as a dodecapolis, the most familiar being the Etruscan League. In ancient Rome, the twelve lictors carried fasces of twelve rods.

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.^[13] 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). The "Twelve Days of Christmas" count the interval between Christmas and Epiphany. Eastern Orthodoxy observes twelve Great Feasts.

The number of twelve jurors in jury trials is depicted by Aeschylus in the Eumenides. In the play, the innovation is brought about by the goddess Athena, who summons twelve citizens to sit as jury. In English Common Law, the tradition of twelve jurors harks back to the 10th-century law code introduced by Aethelred the Unready.

An example from Hinduism are the twelve Jyotirlinga in Shaiva tradition. The Sun god Surya has 12 names. Also, there are 12 Petals in Anahata or "heart chakra". The chief Norse god, Odin, has twelve sons. In the King Arthur Legend, Arthur is said to subdue 12 rebel princes and to win 12 great battles against Saxon invaders^[14]

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

• The lunar year is 12 lunar months. Adding 11 or 12 days completes the solar year.^[15]
• 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

12	Arabic	១២	Khmer	ԺԲ	Armenian
১২	Bangla	ΔΙΙ	Attic Greek
יב	Hebrew		Egyptian
१२	Indian & Nepali (Devanāgarī)	十二	Chinese and Japanese
௧௨	Tamil	Ⅻ	Roman and Etruscan
๑๒	Thai	IIX	Chuvash
౧౨	Telugu	١٢	Urdu
ιβʹ	Ionian Greek	൧൨	Malayalam

In science

• The atomic number of magnesium in the periodic table.
• The Standard Model identifies twelve types of elementary fermions.
• The human body has twelve cranial nerves.
• The duodenum (from Latin duodecim, "twelve") is the first part of the small intestine, that is about twelve inches (30 cm) long. More precisely, this section of the intestine was measured not in inches but in fingerwidths. In fact, in German the name of the duodenum is Zwölffingerdarm and in Dutch the name is twaalfvingerige darm, both meaning "twelve-finger bowel".
• Force 12 on the Beaufort wind force scale corresponds to the maximum wind speed of a hurricane.

In sports

• 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, bowling or keeping wicket).
• 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 European 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 technology

• ASCII and Unicode code point for form feed.
• The number of function keys on most PC keyboards (F1 through F12)
• The number of keys in any standard digital telephone (1 through 9, 0, * and #)
• Microsoft's Rich Text Format specification assigns numbers congruent to 12 mod 256 to variants of the French language.

In the arts

In other fields

12 stars are featured on the Flag of Europe

• 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 of America 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

Wikimedia Commons has media related to 12 (number).

• The Twelfth

Notes

References