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.
As with eleven,[5] the earliest forms of twelve are often considered to be connected with Proto-Germanic Шаблон:Lang or Шаблон:Lang ("to leave"), with the implicit meaning that "two is left" after having already counted to ten.[4] The Lithuanian suffix is also considered to share a similar development.[4] The suffix Шаблон:Lang has also been connected with reconstructions of the Proto-Germanic for ten.[5][6]
As mentioned above, 12 has its own name in Germanic languages such as English (dozen), Dutch (Шаблон:Lang), German (Шаблон:Lang), and Swedish (Шаблон:Lang), all derived from Old French Шаблон:Lang. It is a compound number in many other languages, e.g. Italian Шаблон:Lang (but in Spanish and Portuguese, 16, and in French, 17 is the first compound number),Шаблон:Dubious Japanese 十二 jūni.Шаблон:Clarify
Written representation
In prose writing, twelve, being the last single-syllable 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 ninety-nine or one hundred. Another system spells out all numbers written in one or two words (sixteen, twenty-seven, fifteen thousand, but 372 or 15,001).[7]
In German orthography, there used to be the widely followed (but unofficial) rule of spelling out numbers up to twelve (zwölf). The DudenШаблон:Year needed (the German standard dictionary) mentions this rule as outdated.
Twelve is the number of divisors of 60 and 90, the second and third unitary perfect numbers (6 is the first). It is also the number of distinct prime factors that belong to the fifth unitary perfect number, the largest known,
The densest three-dimensional latticesphere packing has each sphere touching twelve other spheres, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Twelve is also the kissing number in three dimensions.
Fischer group <math>\mathrm {Fi_{22}}</math> is a sporadic group with a total of twelve maximal subgroups, the smallest of which is Mathieu group <math>\mathrm {M_{12}}</math>.[34][35] <math>\mathrm {Fi_{22}}</math> holds standard generators <math>(a,b,ab)</math> equal to (2A, 13, 11),[36] with a further condition where <math>o\bigl((ab)^2 (abab^2)^2 ab^2\bigr) = 12</math>.[37] Furthermore, its faithful complex representation is 78-dimensional,[38] where 78 is the twelfth triangular number.[39] Otherwise, the largest alternating group represented inside any sporadic groups is <math>\mathrm A_{12}</math>, as a maximal subgroup inside the third-largest third generation sporadic group, Harada-Norton group <math>\mathrm {HN}</math>.[40][41] While <math>\mathrm {Fi_{22}}</math> or <math>\mathrm A_{12}</math> are not maximal subgroups of the largest sporadic group, the friendly giant <math>\mathrm {F_{1}}</math>, one of its maximal subgroup is <math>(\mathrm {A_{5}} \times \mathrm {A_{12}}):2</math>.[42] More deeply, the double cover <math>2.\mathrm {Fi_{22}}</math> is a maximal subgroup of <math>\mathrm {Fi_{23}}</math>,[43][44] which is the third-largest maximal subgroup inside <math>\mathrm B</math>;[45][46] with the double cover <math>2.\mathrm B</math> as the largest maximal subgroup inside <math>\mathrm {F_{1}}</math>.[42] The smallest second generation sporadic group, Janko group <math>\mathrm {J_{2}}</math>, holds standard generators (2A, 3B, 7) that yield <math>o\bigl([a,b]\bigr) = 12</math>.[37]
Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant <math>\Delta(q)</math> whose Fourier coefficients are given by the Ramanujan <math>\tau</math>-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 fact that the abelianization of special linear group <math>\operatorname{SL}(2,\mathrm {Z})</math> has twelve elements, to the value of the Riemann zeta function at <math>-1</math> being <math>-\tfrac {1}{12}</math>, which stems from the Ramanujan summation
Although the series is divergent, methods such as Ramanujan summation can assign finite values to divergent series.
12 is an Anti-Meertens Number. If we power the digits from the end to the prime numbers starting from 2 and then multiply, then the result will be the number Itself.
The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.Шаблон:Sfnp
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.
Judaism and Christianity
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.[48] 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. Шаблон:Bibleverse-nb 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 (the Tribe of Dan is omitted while Manasseh is mentioned), making a total of 144,000 (which is the square of 12 multiplied by a thousand).
12 was the only number considered to be religiously divine in the 1600s causing many Catholics to wear 12 buttons to church every Sunday. Some extremely devout Catholics would always wear this number of buttons to any occasion on any type of clothing.Шаблон:Citation needed
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.
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.
The duodenum (from Шаблон:Lang-la) 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, in Dutch the name is twaalfvingerige darm and in Bulgarian the name is дванадесетопръстник, all meaning "twelve-finger bowel".
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. It also serves as the jersey number for some the National Football League's best and most well-known quarterback, Tom Brady.
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 or bowling).
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 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.
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 gods of Kobol. In the re-imagined series, there are also twelve models of humanoid Cylons.
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.
12 is the maximum score a competing entry can receive by each country in the Eurovision Song Contest.
Art theory
There are twelve basic hues in the color wheel: three primary colors (red, yellow, blue), three secondary colors (orange, green & purple) and six 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 come-out roll constitutes a "craps" and the shooter (dice thrower) loses immediately.
Games such as Backgammon have a long history of 12 points on each side of the gaming board, as evidenced in the XII scripta board in the museum at Ephesus.[51]
12 is the last number featured on the analogue clock, and also the starting point of the transition from A.M. to P.M. hours or vice-versa.
There are twelve months within a year, with the last one being December.
The level of grades in which one must attend school typically ends at 12 (although some jurisdictions may include a thirteenth grade depending on the country).Шаблон:Citation needed
Twelve hours form half a day, and twelve hours away from another lead to the same time but with a different period (ex. Twelve hours away from 6:00 AM leads to 6:00 PM).
There are normally twelve pairs of ribs in the human body.
The Twelve Tables or Leges 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.
The United States 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.
"The reader should note that each of Wilson's frames [Wilson 82] contains three of ours, with 3 · 48 = 144 vectors, and has slightly larger stabilizer."
↑"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 breast-plate, by the twelve loaves of the shew-bread, 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.
