Definitions

# 12 (number)

 Mathematical properties φ(12) = 4 τ(12) = 6 σ(12) = 28 π(12) = 5 μ(12) = 0 M(12) = -2

12 (twelve) is the natural number following 11 and preceding 13.

The word "twelve" is a native English word that presumably arises from the Germanic compound twa-lif "two-leave", meaning that two is left before one takes away the base, ten. This compound meaning may have been transparent to speakers of Old English, but the modern form "twelve" is quite translucent. Only the remaining tw- hints that twelve and two are related. Etymology (Weekley, Skeat) suggests that "twelve" (similar to "eleven") consists of two parts, the first meaning "two" and the second "leftover", so a literal translation would yield "two remaining [after having ten taken]".

A group of twelve things is called a Duodecad. The ordinal adjective is duodenary, twelfth. The adjective referring to a group consisting of twelve things is duodecuple.

The number twelve is often used as a sales unit in trade, and is often referred to as a dozen. Twelve dozen are known as a gross. (Note that there are thirteen items in a baker's dozen.)

As shown below, the number twelve is frequently referenced in the Abrahamic religions and is also central to Western calendar and units of time.

## In mathematics

Twelve is a composite number, the smallest number with exactly six divisors, its proper divisors being 1, 2, 3, 4 and 6. Twelve is also a highly composite number, the next one being 24. It is the first composite number of the form p2q; a square prime, and also the first member of the (p2) family in this form. 12 has an aliquot sum of 16 (133% in abundance). Accordingly, 12 is the first abundant number (in fact a superabundant number) and demonstrates an 8 member aliquot sequence; {12,16,15,9,4,3,1,0} 12 is the 3rd composite number in the 3-aliquot tree. The only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant (18 and 20).

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.

Twelve is a superfactorial, being the product of the first three factorials. Twelve being the product of three and four, the first four positive integers show up in the equation 12 = 3 × 4, which can be continued with the equation 56 = 7 × 8.

Twelve is the ninth Perrin number, preceded in the sequence by 5, 7, 10. It is the fourth Pell number, preceded in the sequence by 2 and 5 (it is the sum of the former plus twice the latter).

A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron. 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 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.

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

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 50 100 1000
$12 times x$ 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 300 600 1200 12000

## In numeral systems

١٢ ԺԲ ιβ´ Arabic Armenian Ionian Greek Attic Greek Hebrew V20-Z1-Z1 Egyptian Indian (Devanāgarī) Chinese and Japanese Tamil Roman and Etruscan Thai Chuvash

## In science

Magnesium dioxide dissovles at 12oc

## In religion

The number 12 is very important in many religions, mainly Judaism and Christianity, but some uses are to be found in pagan times.

In Shi'a Islam, there are twelve Imams, legitimate successors of the prophet Muhammad. These twelve early leaders of Islam are—Ali, Hasan, Husayn, and nine of Husayn's descendants.

In Antiquity there are numerous magical/religious uses of twelves. Ancient Greek religion, the Twelve Olympians were the principal gods of the pantheon. The chief Norse god, Odin, had 12 sons. Several sets of twelve cities are identified in history as a dodecapolis, the most familiar being the Etruscan League. In the King Arthur Legend, Arthur is said to have subdued 12 rebel princes and to have won 12 great battles against Saxon invaders. [source: Benet's Reader's Encyclopedia, 3d ed]

The importance of 12 in Judaism and Christianity can be found in the Bible. The biblical Jacob had 12 sons, who were the progenitors of the Twelve Tribes of Israel, while the New Testament describes twelve apostles of Jesus; when Judas Iscariot was disgraced, a meeting was held (Acts) to add Matthias to complete the number twelve once more. (Today, The Church of Jesus Christ of Latter-day Saints has a Quorum of the Twelve Apostles.)

The Book of Revelation contains much numerical symbolism, and a lot of the numbers mentioned have 12 as a divisor. mentions a woman — interpreted as the people of Israel, the Church or 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).

There are 12 days of Christmas. The song Twelve Days of Christmas came from the traditional practice of extending Yuletide celebrations over the twelve days from Christmas day to the eve of Epiphany; the period of thirteen days including Epiphany is sometimes known as Christmastide. Thus Twelfth Night is another name for the twelfth day of Christmas or January 5 (the eve of Epiphany). Similarly, Eastern Orthodoxy observes 12 Great Feasts.

In Judaism, 12 signifies the age a girl matures .

## In time

• Most calendar systems have twelve months in a year.
• The Western zodiac has twelve signs, as does the Chinese zodiac.
• The Chinese use a 12 years cycle for time-reckoning called Earthly Branches.
• There are twenty-four hours in a day in all, with twelve hours for a half a day. The hours are numbered from one to twelve for both the ante meridiem (a.m.) half of the day and the post meridiem (p.m.) half of the day. 12:00 after a.m. and before p.m. (in the middle of the day) is midday or noon, and 12:00 after p.m. and before a.m. (in the middle of the night) is midnight. A new day is considered to start with the stroke of midnight. Furthermore, the basic units of time (60 seconds, 60 minutes, 24 hours) can all perfectly divide by twelve.
• The minute hand of a clock face turns twelve times as fast as the hour hand.

## In sports

In rugby union one of the centres, most often but not always the inside centre, wears the 12 shirt, while in rugby league, one of the second-row forwards wears the number 12 jersey.

In both soccer and American Football, the number 12 is 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, Flamengo and the Seattle Seahawks do not allow field players to wear the number 12 on their jersey because it is reserved for their supporters.

## In the arts

### Film

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

### Art Theory

• 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

• Twelve is a character in the Street Fighter video game
• The Roman form of 12 (XII) is used as the symbol of the organization MJ12 in the Deus Ex computer game.

## In other fields

• There are 12 in a dozen.
• There are 12 ounces in a troy pound (used for precious metals), and 12 constellations in the ecliptic (or signs of the zodiac).
• In the former British currency system, there were twelve pence in a shilling.
• In astrology, there are 12 signs in the Zodiac.
• In Greek mythology, the number of labours of Heracles was increased from ten to make twelve.
• The number of dan (master) grades in judo.
• 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.
• Twelve stars are featured on the European flag.
• The car number of NASCAR's Ryan Newman.
• 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) 12 Angry Men.
• Twelve men have walked on the 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.
• Butterfree is the Twelfth Pokémon according to the National Pokedex.
• 12 is the number of the French department Aveyron

## Historical years

12 A.D., 12 B.C., 1912, 2012, etc.