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  
Greek prefix  dodeca  
Latin prefix  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 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.
Contents
Name[edit]
Twelve is the largest number with a singlesyllable name in English. Early Germanic numbers 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.^{[1]}^{[2]}^{[3]} Such uses gradually disappeared with the introduction of Arabic numerals during the 12thcentury Renaissance.
It derives from the Old English twelf and tuelf, first attested in the 10thcentury Lindisfarne Gospels' Book of John.^{[n 1]}^{[5]} It has cognates in every Germanic language (e.g. German zwölf), whose ProtoGermanic 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 IndoEuropean 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 base12 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 ProtoGermanic *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 ProtoGermanic 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 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 either nine, ten or twelve, or even ninetynine or one hundred. Another system spells out all numbers written in one or two words (sixteen, twentyseven, fifteen thousand, but 372 or 15,001).^{[citation needed]} 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 twentyfour.^{[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 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 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 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 (12_{10} [twelve] = 10_{12}), 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]
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  

12 × 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  

12 ÷ x  12  6  4  3  2.4  2  1.714285  1.5  1.3  1.2  1.09  1  0.923076  0.857142  0.8  0.75  
x ÷ 12  0.083  0.16  0.25  0.3  0.416  0.5  0.583  0.6  0.75  0.83  0.916  1  1.083  1.16  1.25  1.3 
Exponentiation  1  2  3  4  5  6  7  8  9  10  11  12  13  

12^{x}  12  144  1728  20736  248832  2985984  35831808  429981696  5159780352  61917364224  743008370688  8916100448256  106993205379072  
x^{12}  1  4096  531441  16777216  244140625  2176782336  13841287201  68719476736  282429536481  1000000000000  3138428376721  8916100448256  23298085122481 
Religion[edit]
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.
Ancient Greek religion[edit]
 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.
Christianity[edit]
 The significance is especially pronounced in the Hebrew 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.^{[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 10thcentury law code introduced by Aethelred the Unready.
Hinduism[edit]
 There are twelve Jyotirlinga(Selfformed Lingas) of Lord Shiva in 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[edit]
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[edit]
 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 12year cycle for timereckoning 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]
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[edit]
 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 "twelvefinger bowel".
 Force 12 on the Beaufort wind force scale corresponds to the maximum wind speed of a hurricane.
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 walkon 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 secondrow 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 technology[edit]
 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[edit]
Film[edit]
Movies with the number twelve or its variations in their titles include
 12
 12 Angry Men (1957 and 1997)
 Cheaper by the Dozen
 Ocean's Twelve
 12 Monkeys
 The Dirty Dozen
 The Twelve Chairs (1970, 1971 and 1976)
 12 Rounds
 Twelve
 Twelve Years a Slave
Television[edit]
 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 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 series Studio One
 "Number 12 Looks Just Like You" is an episode of the television show The Twilight Zone.
 Schoolhouse Rock! portrayed an alien child using basetwelve arithmetic in the short "Little Twelvetoes".
 12 oz. Mouse was an animated television show on Adult Swim.
 The News 12 Networks are a group of American regional cable news television channels covering New York and New Jersey.
 Les 12 Coups De Midi is a French game show broadcast on TF1 with Oliver Minne.
Theatre[edit]
 Twelfth Night is a comedy by William Shakespeare
 The Vision of the Twelve Goddesses is a Jacobean masque by Samuel Daniel
 Twelve Angry Men, by Reginald Rose, adapted from his own teleplay (see above)
Literature[edit]
 The Twelve is a poem by Aleksandr Blok
 Twelve 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
 The Twelve Dancing Princesses is a folk tale
 The Aeneid, an epic poem by Virgil is divided into two halves composed of twelve books.
 Paradise Lost, an epic poem by John Milton is divided into twelve books perhaps in imitation of the Aeneid
 Miguel de Cervantes wrote twelve Novelas ejemplares
Music[edit]
Music theory[edit]
 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 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[edit]
 The 12inch single is a vinyl record format.
 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", a Song from the album Brave Murder Day by Katatonia.
 12 is a studio album by German singer Herbert Grönemeyer.
 Twelve is an album by Patti Smith.
 Twelve Deadly Cyns...and Then Some is 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 their Savior Sorrow album.
 12 is 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[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 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 the Street Fighter video game series.
 In Mario Kart Wii and Mario Kart 8, the starting grid can carry twelve characters.
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 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[edit]
Wikimedia Commons has media related to 12 (number). 
Notes[edit]
 ^ Specially, a passage referring to Judas Iscariot as "one of the twelve" (an of ðæm tuelfum).^{[4]}
References[edit]
Citations[edit]
 ^ Gordon, E V (1957). Introduction to Old Norse. Oxford: Claredon Press. pp. 292–293.
 ^ Stevenson, W. H. (December 1899). "The Long Hundred and its Use in England". Archaeological Review. 4 (5): 313–317.
 ^ Goodare, Julian (1993). "The Long Hundred in medieval and early modern Scotland" (PDF). Proceedings of the Society of Antiquaries of Scotland. 123: 395–418.
 ^ John 6:71.
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} Oxford English Dictionary, 1st ed. "twelve, adj. and n." Oxford University Press (Oxford), 1916.
 ^ ^{a} ^{b} Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
 ^ Dantzig, Tobias (1930), Number: The Language of Science.
 ^ "Sloane's A002182 : Highly composite numbers". The OnLine Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20160601.
 ^ "Sloane's A081357 : Sublime numbers". The OnLine Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20160601.
 ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The OnLine Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20160601.
 ^ Drews (1972), p. 43, n. 10.
 ^ Weinreich, Th., "Zwölfgötter", Ausführliches Lexikon der Griechischen und Römischen Mythologie, Vol. VI, col. 764848.
 ^ "And it is thought that there is a special significance in the number twelve. It was typified, we know, by many things in the Old Testament ; by the twelve sons of Jacob, by the twelve princes of the children of Israel, by the twelve fountains in Elim, by the twelve stones in Aaron's breastplate, by the twelve loaves of the shewbread, by the twelve spies sent by Moses, by the twelve stones of which the altar was made, by the twelve stones taken out of Jordan, by the twelve oxen which bare" P. Young, Daily readings for a year (1863), p. 150.
 ^ Benet's Reader's Encyclopedia, 3d ed.
 ^ "Lunar versus solar calendar".
Bibliography[edit]
 Drews, Robert (January 1972), "Light from Anatolia on the Roman Fasces", The American Journal of Philology, Vol. 93, No. 1, pp. 40–51.
 Lattice Polygons and the Number 12, Bjorn Poonen, Fernando RodriguezVillegas, American Mathematical Monthly, Vol. 107, No. 3 (March, 2000), pp. 238–250 [1]
 Schwartzman, Steven (1994). The words of mathematics: An etymological dictionary of mathematical terms used in English. The Mathematical Association of America. ISBN 0883855119.