12 (number)
12 (number)



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Cardinal  twelve  
Ordinal  12th (twelfth) 

Numeral system  duodecimal  
Factorization  2^{2}× 3  
Divisors  1, 2, 3, 4, 6, 12  
Greek numeral  ΙΒ´  
Roman numeral  XII  
Greekprefix  dodeca  
Latinprefix  duodeca  
Binary  1100_{2}  
Ternary  110_{3}  
Quaternary  30_{4}  
Quinary  22_{5}  
Senary  20_{6}  
Octal  14_{8}  
Duodecimal  10_{12}  
Hexadecimal  C_{16}  
Vigesimal  C_{20}  
Base 36  C_{36}  
Mathematical properties  
φ(12) = 4  τ(12) = 6  
σ(12) = 28  π(12) = 5  
μ(12) = 0  M(12) = 2 
12(twelve) is thenatural numberfollowing 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 theWestern calendarand units of time of day, and frequently appears in the world’s major religions.



← 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  12th (twelfth) 

Numeral system  duodecimal  
Factorization  2^{2}× 3  
Divisors  1, 2, 3, 4, 6, 12  
Greek numeral  ΙΒ´  
Roman numeral  XII  
Greekprefix  dodeca  
Latinprefix  duodeca  
Binary  1100_{2}  
Ternary  110_{3}  
Quaternary  30_{4}  
Quinary  22_{5}  
Senary  20_{6}  
Octal  14_{8}  
Duodecimal  10_{12}  
Hexadecimal  C_{16}  
Vigesimal  C_{20}  
Base 36  C_{36}  
Mathematical properties  
φ(12) = 4  τ(12) = 6  
σ(12) = 28  π(12) = 5  
μ(12) = 0  M(12) = 2 
Name
Twelve is the largest number with a singlesyllable name inEnglish. EarlyGermanicnumbers have been theorized to have been nondecimal: 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 “tencount” in medieval texts showing that writers could not presume their readers would normally understand them that way.^{[2]}^{[3]}^{[4]}Such uses gradually disappeared with the introduction of Arabic numerals during the 12thcentury Renaissance.
It derives from theOld Englishtwelfandtuelf, first attested in the 10thcentury Lindisfarne Gospels’ Book of John.^{[1]}^{[6]}It has cognates in every Germanic language (e.g. Germanzwölf), whose ProtoGermanic ancestor has been reconstructed as **twaliƀi…*, from *twa(“two”) and suffix *lifor *liƀof uncertain meaning.^{[6]}It is sometimes compared with the Lithuaniandvýlika, althoughlikais used as the suffix for all numbers from 11 to 19 (analogous to “teen”).^{[6]}Every other IndoEuropean language instead uses a form of “two”+”ten”, such as theLatinduōdecim.^{[6]}The usual ordinal form is “twelfth” but “dozenth” or “duodecimal” (from the Latin word) is also used in some contexts, particularly base12 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,^{[7]}the earliest forms of twelve are often considered to be connected with ProtoGermanic *liƀanor *liƀan(“to leave”), with the implicit meaning that “two is left” after having already counted to ten.^{[6]}The Lithuanian suffix is also considered to share a similar development.^{[6]}The suffix *lifhas also been connected with reconstructions of the ProtoGermanic for ten.^{[7]}^{[8]}
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. Italiandodici(but in Spanish and Portuguese, 16, and in French, 17 is the first compound number), Japanese 十二jūni.
Written representation
In prose writing,twelve, being the last singlesyllable 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 eithernine,tenortwelve, or evenninetynineorone hundred. Another system spells out all numbers written in one or two words (sixteen,twentyseven,fifteen thousand, but372or15,001). In German orthography, there used to be the widely followed (but unofficial) rule of spelling out numbers up to twelve (zwölf). The Duden (the German standard dictionary) mentions this rule as outdated.
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 twentyfour.^{[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 twelvesided polygon is a dodecagon. A twelvefaced 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 threedimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true foranyarrangement 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 τfunction 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 distancetransitive 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 fromMesopotamia.
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  23  24  25  50  100  1000  

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 
Division  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  

x  12  6  4  3  2.4  2 
714285 
1.5 
3 
1.2 
09 
1 
923076 
857142 
0.8  0.75  
x**  0.083  0.16  0.25 
3 
0.416  0.5  0.583 
6 
0.75  0.83  0.916  1  1.083  1.16  1.25 
3 
Exponentiation  1  2  3  4  5  6  7  8  9  10  11  12  13  

x  12  144  1728  20736  248832  2985984  35831808  429981696  5159780352  61917364224  743008370688  8916100448256  106993205379072  
x  1  4096  531441  16777216  244140625  2176782336  13841287201  68719476736  282429536481  1000000000000  3138428376721  8916100448256  23298085122481 
In nature
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.
Religion
The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.^{[12]}
Ancient Greek religion

The Twelve Olympians are the principal gods of the pantheon, they were preceded by twelve Titans, and Hercules carries out twelve labours.^{[13]}

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.
Christianity

The significance is especially pronounced in theHebrew Bible.
Ishmael – the firstborn 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^{[19]}mentions a woman—interpreted as the people of Israel, theChurchand 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 theEumenides. 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 10thcentury law code introduced by Aethelred the Unready.
Hinduism

There are twelve Jyotirlinga(Selfformed Lingas) of LordShivain Hindu temples across India according to the Shaiva tradition.

The Sun god Surya has 12 names.

There are 12 Petals in Anahata or “heart chakra”.

There are frequently said to be 12 Âdityas.
Others

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.^{[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 theQuranis 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.^{[16]}

Most calendar systems – solar or lunar – have twelve months in ayear.

The Chinese use a 12year cycle for timereckoning called Earthly Branches.

There are twelve hours in a half day, numbered one to twelve for both theante meridiem(a.m.) and thepost 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 and Nepali (Devanāgarī)  十二  Chinese and Japanese  
௧௨  Tamil  Ⅻ  Romanand Etruscan  
๑๒  Thai  IIX  Chuvash  
౧౨  Telugu  ١٢  Urdu  
ιβʹ  Ionian Greek  ൧൨  Malayalam 
In science

The atomic number ofmagnesiumin the periodic table.

The Standard Model identifies twelve types of elementaryfermions.

The human body has twelve cranial nerves.

The duodenum (from Latinduodecim,“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, inGermanthe name of the duodenum isZwölffingerdarmand inDutchthe name istwaalfvingerige darm, both meaning “twelvefinger bowel”.

Force 12 on the Beaufort wind force scale corresponds to the maximum wind speed of a hurricane.
In sports

In both soccer andAmerican 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 walkon player who represents the original “12th Man”, a fan who was asked to play when the team’s reserves were low in a collegeAmerican footballgame 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.

Incricket, 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.

Inrugby league, one of the starting secondrow forwards wears the number 12 jersey in most competitions. An exception is in the Super League, which uses static squad numbering.

Inrugby union, one of the starting centres, most often but not always the inside centre, wears the 12 shirt.

In anNBAgame, a quarter lasts 12 minutes.
In technology

ASCII andUnicodecode 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 theFrench language.
In the arts
Film
Movies with the number twelve or its variations in their titles include:

12

12 Angry Men(1957 and 1997)

Cheaper by the Dozen

12 Monkeys

The Dirty Dozen

The Twelve Chairs(1970, 1971 and 1976)

12 Rounds

Twelve

Twelve Years a Slave
Television

The number twelve plays a significant role in the television franchiseBattlestar Galactica. The characters come from the Twelve Colonies of Kobol and worship the twelve lords of Kobol. In the reimagined series, there are also twelve models of the humanoid version of Cylons.

Twelve Angry Men, the original 1954 live performance on the anthology television seriesStudio One

“Number 12 Looks Just Like You” is an episode of the television showThe Twilight Zone.

Schoolhouse Rock!portrayed an alien child using basetwelve arithmetic in the short “Little Twelvetoes”^{[20]}.

12 oz. Mousewas an animated television show onAdult Swim.

The News 12 Networks are a group of American regional cable news television channels covering New York, New Jersey, and Connecticut.

Les 12 Coups de Midiis a French game show broadcast on TF1 with Oliver Minne at midday.
Theatre

Twelfth Nightis a comedy byWilliam Shakespeare.

The Vision of the Twelve Goddessesis a Jacobean masque by Samuel Daniel.

Twelve Angry Men, by Reginald Rose, adapted from his own teleplay (see above).
Literature

The Twelveis a poem by Aleksandr Blok.

Twelveis a novel by Nick McDonell.

The Twelve Chairsis a satirical novel by the Soviet authors Ilf and Petrov.

Cheaper by the Dozenis a 1946 novel by Frank Bunker Gilbreth, Jr. and Ernestine Gilbreth Carey.

The Twelve Dancing Princessesis a folk tale.

TheAeneid, an epic poem byVirgilis divided into two halves composed of twelve books.

Paradise Lost, an epic poem byJohn Miltonis divided into twelve books perhaps in imitation of theAeneid.

Miguel de Cervantes wrote twelveNovelas ejemplares.
Music
Music theory

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 theclarinetwhich behave as a stopped cylindrical pipe overblow at the twelfth.

The twelvetone technique (also dodecaphony) is a method of musical composition devised by Arnold Schoenberg. Music using the technique is called twelvetone music.

The Twelvebar blues is one of the most prominent chord progressions in popular music.

12inch record, see Phonograph record#78 rpm disc sizes.
Pop music

The 12inch single is a vinyl record format.

Twelfth Night is a progressive rock band.

12 Playis an R. Kelly album.

The Number 12 Looks Like You is a mathcore band.

“12”, a Song from the albumBrave Murder Dayby Katatonia.

12is a studio album by German singer Herbert Grönemeyer.

Twelveis an album by Patti Smith.

Twelve Deadly Cyns…and Then Someis an album by Cyndi Lauper.

D12 a rap group also known as the Dirty Dozen.

12 Stones is an American Christian rock band.

“12 Hundred” is a song by band Mushroomhead of theirSavior Sorrowalbum.

12is the 12th studio album by Keller Williams.

“12” (“Dodeka” in Greek) is one of the most wellknown hits by Anna Vissi.

“Twelve drummers drumming” is the gift on the twelfth day of Christmas in the carol “The Twelve Days of Christmas”.

Twelve Girls Band are an all female Chinese musical group .

*12 (American Song Book)*is an album by Italian singer Mina.

Revelation #12 is a song by American rock band Marilyn Manson.
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

In the game of craps, a dice roll of two sixes (value 12) on the comeout roll constitutes a “craps” and the shooter (dice thrower) loses immediately.

Twelve is a character in theStreet Fightervideo game series.
In other fields

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.

InGreek 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 onesyllable.

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 underlyingRoman law.

In theUnited States, twelve people are appointed to sit on ajuryfor 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.

TheUnited States of Americais 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. PresidentHarry S. Trumanto 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

The Twelfth