12 (number)

← 11 12 13 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	twelve
Ordinal	th
Numeral system	duodecimal
Factorization	$2^{2}\cdot 3$
Divisors	1, 2, 3, 4, 6, 12
Greek numeral	ΙΒ´
Roman numeral	XII
Binary	11002
Ternary	1103
Senary	206
Octal	148
Duodecimal	1012
Hexadecimal	C16

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	Arabic	ԺԲ	Armenian
ιβ´	Ionian Greek	ΔΙΙ	Attic Greek
יב	Hebrew		Egyptian
१२	Indian (Devanāgarī)	十二	Chinese and Japanese
௧௨	Tamil	Ⅻ	Roman and Etruscan
๑๒	Thai	IIX	Chuvash

In science

• The atomic number of magnesium
• There are twelve cranial nerves
• The duodenum (from Latin duodecim, "twelve") is the first part of the small intestine, that is about twelve inches 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, meaning "twelve-finger bowel."
• Force 12 on the Beaufort wind force scale corresponds to the maximum wind speed of a hurricane.

Magnesium dioxide dissovles at 12oc

Astronomy

• Messier object M12, a magnitude 8.0 globular cluster in the constellation Ophiuchus
• The New General Catalogue object NGC 12, a magnitude 13.1 spiral galaxy in the constellation Pisces
• The Saros number of the solar eclipse series which began on 2680 BC August 8 and ended on 1129 BC February 25. The duration of Saros series 12 was 1550.5 years, and it contained 87 solar eclipses.
• The Saros number of the lunar eclipse series which began on 2360 BC May 28 and ended on 1062 BC July 17. The duration of Saros series 12 was 1298.1 years, and it contained 73 lunar eclipses.
• The 12th moon of Jupiter is Lysithea.

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 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. 12:1 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 (bat mitzvah).

In the largest branch of Shi'a Islam, the Twelvers, there are twelve Imams. These twelve early leaders of Islam are—Ali, Hasan, Husayn, and nine of Husayn's descendants.

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

• American baseball player, Graig Nettles, wore number 12 for the Cleveland Indians (1970-72).
• In rugby union one of the centres, most often but not always the inside centre, wears the 12 shirt.
• One popular jersey number of American football quarterbacks, like Roger Staubach, Chris Chandler, Randall Cunningham, Rich Gannon, Ken Stabler, Bob Griese, Greg Cook, Jim Kelly, The Legend Shroom Reznik, Joe Namath, Terry Bradshaw, and Tom Brady. It's also the number worn by hockey players Sid Abel and Ryan Malone, and Eric Staal.
• Jersey Number of Basketball Point guards, like John Stockton, Kirk Hinrich, Rafer Alston
• 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.
• Jersey number of Dwight Howard of the Orlando Magic. Jersey number of LaMarcus Aldridge of the Portland Trail Blazers.
• 12 Professional Paintball teams will battle during the 2008 NXL season for Glory, Honor and Respect.
• Brian Roll of the softball team Rush City VFW wears the number 12. The team is out of Rush City, MN.

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 dialling 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

Film

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

• 12
• 12 Angry Men (film)
• Cheaper by the Dozen
• Ocean's Twelve
• 12 Monkeys

Television

• The number twelve plays a significant role in the television franchise Battlestar Galactica. The characters come from the Twelve Colonies of Kobol and worship the twelve lords of Kobol. In the re-imagined series, there are also twelve models of the humanoid version of Cylons.
• Number 12 Looks Just Like You is an episode of the Television show "The Twilight Zone".
• Schoolhouse Rock! portrayed an alien child using base-twelve arithmetic in the short "Little Twelvetoes".

Theatre

• Twelfth Night is a comedy by William Shakespeare

Literature

• The Twelve is a poem by Aleksandr Blok
• Twelve (novel) is a novel by Nick McDonell
• The Twelve Chairs is a satirical novel by the Soviet authors Ilf and Petrov
• Cheaper by the Dozen is a 1946 novel by Frank Bunker Gilbreth, Jr. and Ernestine Gilbreth Carey

Music

• 12 is the third album by German band The Notwist
• Twelve Girls Band
• Twelve is the number of pitch classes in an octave, not counting the duplicated (octave) pitch. Also, the total number of major keys, (not counting enharmonic equivalents) and the total number of minor keys (also not counting equivalents). This applies only to twelve tone equal temperament, the most common tuning used today in western influenced music.
• The twelfth is the interval of an octave and a fifth. Instruments such as the clarinet which behave as a stopped cylindrical pipe overblow at the twelfth.
• The twelve-tone technique (also dodecaphony) is a method of musical composition devised by Arnold Schoenberg. Music using the technique is called twelve-tone music.
• Twelfth Night is a progressive rock band
• 12 Play is an R. Kelly album.
• The Number 12 Looks Like You is a mathcore band.
• 12 is a studio album by German singer Herbert Grönemeyer.
• Twelve Deadly Cyns...and Then Some is an album by Cyndi Lauper.
• D12 a rap group also known as the Dirty Dozen.
• Musical group named 12 Stones
• 12 Hundred is a song by band Mushroomhead off their Savior Sorrow album.
• 12 is the 12th studio album by Keller Williams.

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 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.

Historical years

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

See also

• Twelve
• The Twelfth
• 12

References

• Schwartzman, Steven (1994). The words of mathematics: An etymological dictionary of mathematical terms used in English. The Mathematical Association of America. ISBN 0-88385-511-9.
• Lattice Polygons and the Number 12, Bjorn Poonen, Fernando Rodriguez-Villegas, American Mathematical Monthly, Vol. 107, No. 3 (Mar., 2000) , pp. 238-250 [1]

External links

• This Week's Finds in Mathematical Physics Week 125 (discusses "12-ness" of SL(2,Z))
• http://www.number12secret.com
• Why twelve Article on the number 12
• The Number Twelve Looks Like You