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.
Derived from Old English, twelf and tuelf are first attested in the 10th-century Lindisfarne Gospels' Book of John.[note 1][5] It has cognates in every Germanic language (e.g. German zwölf), whose Proto-Germanic ancestor has been reconstructed as *twaliƀi..., from *twa ("two") and suffix *-lif- or *-liƀ- of uncertain meaning.[5] It is sometimes compared with the Lithuaniandvýlika, although -lika is used as the suffix for all numbers from 11 to 19 (analogous to "-teen").[5] Every other Indo-European language instead uses a form of "two"+"ten", such as the Latinduōdecim.[5] The usual ordinal form is "twelfth" but "dozenth" or "duodecimal" (from the Latin word) is also used in some contexts, particularly base-12 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,[6] the earliest forms of twelve are often considered to be connected with Proto-Germanic *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 Proto-Germanic for ten.[6][7]
As mentioned above, 12 has its own name in Germanic languages such as English (dozen), Dutch (dozijn), German (Dutzend), and Swedish (dussin), all derived from Old French dozaine. 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
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).[8]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
12 is the sixth composite number and the superfactorial of 3.[9][10] It is the fourth pronic number (equal to 3 × 4),[11] whose digits in decimal are also successive. It 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,[12] and the second semiperfect number, since there is a subset of the proper divisors of 12 that add up to itself.[13] It is equal to the sum between the second pair of twin primes (5 + 7),[14] while it is also the smallest number with exactly six divisors (1, 2, 3, 4, 6 and 12) which makes it the fifth highly composite number,[15] and since 6 is also one of them, twelve is also the fifth refactorable number.[16] 12, as a number with a perfect number of divisors (six), has a sum of divisors that yields the second perfect number, σ(12) = 28,[17] and as such it is the smallest of two known sublime numbers, which are numbers that have a perfect number of divisors whose sum is also perfect.[18] 12 is the fifth Pell number (preceded by 0, 1, 2, and 5)[19] as well as the third pentagonal number,[20] and a Harshad number in all bases except octal.
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 is a sporadic group with a total of twelve maximal subgroups, the smallest of which is Mathieu group.[35][36] holds standard generators equal to (2A, 13, 11),[37] with a further condition where .[38] Furthermore, its faithful complex representation is 78-dimensional,[39] where 78 is the twelfth triangular number.[40] Otherwise, the largest alternating group represented inside any sporadic groups is , as a maximal subgroup inside the third-largest third generation sporadic group, Harada-Norton group.[41][42] While or are not maximal subgroups of the largest sporadic group, the friendly giant, one of its maximal subgroup is .[43] More deeply, the double cover is a maximal subgroup of ,[44][45] which is the third-largest maximal subgroup inside ;[46][47] with the double cover as the largest maximal subgroup inside .[43] The smallest second generation sporadic group, Janko group, holds standard generators (2A, 3B, 7) that yield .[38]
Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant whose Fourier coefficients are given by the Ramanujan-function and which is (up to a constant multiplier) the 24th power of the Dedekind eta function:
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.[48]
Altar of the Twelve Gods to whom the Altar was dedicated is uncertain, but they were most likely substantially the same as the twelve Olympian gods represented on the east frieze of the Parthenon.
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.[50] 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 (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.[citation needed]
And ˹remember˺ when Moses prayed for water for his people, We said, "Strike the rock with your staff." Then twelve springs gushed out, ˹and˺ each tribe knew its drinking place. ˹We then said,˺ "Eat and drink of Allah’s provisions, and do not go about spreading corruption in the land."
We divided them into twelve tribes—each as a community. And We revealed to Moses, when his people asked for water, "Strike the rock with your staff." Then twelve springs gushed out. Each tribe knew its drinking place. We shaded them with clouds and sent down to them manna and quails,1 ˹saying˺, "Eat from the good things We have provided for you." They ˹certainly˺ did not wrong Us, but wronged themselves.
Note 1: Manna (heavenly bread) and quails (chicken-like birds) sustained the children of Israel in the wilderness after they left Egypt.
The third reference is to the number of months and the sacred ones amongst them:
Indeed, the number of months with Allāh is twelve [lunar] months in the register of Allāh [from] the day He created the heavens and the earth; of these, four are sacred.2
In the King Arthurlegend, Arthur is said to subdue 12 rebel princes and to win 12 great battles against Saxon invaders.[55]
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.
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.
Most calendar systems – solar or lunar – have twelve months in a year.
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 Latin: duodecim, lit. '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, 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.
In an NBA game, a quarter lasts 12 minutes.
In pool:
The pool ball 12 is the 12th in pool and its color is purple.
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.
Apocalypse: The Twelve, a comic book crossover in Marvel Comics. The connection between Apocalypse and twelve specific mutants is revisitied in the 2024 limited series, X-Men: Heir to Apocalypse.
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 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.[57]
In other fields
There are 12 troy ounces in a troy pound (used for precious metals).
In English, twelve is the number of greatest magnitude that has just one syllable.
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).[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.
^Specially, a passage referring to Judas Iscariot as "one of the twelve" (an of ðæm tuelfum).[4]
References
^Gordon, E. V. (1957). Introduction to Old Norse. Oxford, England: Clarendon Press. pp. 292–293. Archived from the original on 2016-04-15. Retrieved 2017-09-08.
^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. doi:10.9750/PSAS.123.395.418. S2CID 162146336.
^John 6:71.
^ a b c d e fOxford English Dictionary, 1st ed. "twelve, adj. and n." Oxford University Press (Oxford), 1916.
^ a bOxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
^Dantzig, Tobias (1930), Number: The Language of Science.
^Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers, definition (1): numbers n where d(n), the number of divisors of n (A000005), increases to a record.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-19.
^Wall, Charles R. (1988). "New unitary perfect numbers have at least nine odd components" (PDF). Fibonacci Quarterly. 26 (4): 312. ISSN 0015-0517. MR 0967649. Zbl 0657.10003.
^Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers: numbers n such that the harmonic mean of the divisors of n is an integer.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
^Pace P., Nielsen (2007). "Odd perfect numbers have at least nine distinct prime factors". Mathematics of Computation. 76 (260). Providence, R.I.: American Mathematical Society: 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. MR 2336286. S2CID 2767519. Zbl 1142.11086.
^Grünbaum, Branko; Shephard, G. C. (1987). "Section 2.1: Regular and uniform tilings". Tilings and Patterns. New York: W. H. Freeman and Company. p. 59. doi:10.2307/2323457. ISBN 0-7167-1193-1. JSTOR 2323457. OCLC 13092426. S2CID 119730123.
^H. S. M. Coxeter (1991). Regular Complex Polytopes (2 ed.). Cambridge University Press. pp. 144–146. doi:10.2307/3617711. ISBN 978-0-521-39490-1. JSTOR 3617711. S2CID 116900933. Zbl 0732.51002.
^Weber, Matthias (2005). "Kepler's small stellated dodecahedron as a Riemann surface" (PDF). Pacific Journal of Mathematics. 220 (1): 172. doi:10.2140/pjm.2005.220.167. MR 2195068. S2CID 54518859. Zbl 1100.30036.
^Wilson, Robert A. (1982). "The Quaternionic Lattice for 2G2(4) and its Maximal Subgroups". Journal of Algebra. 77 (2). Elsevier: 451–453. doi:10.1016/0021-8693(82)90266-6. MR 0673128. S2CID 120032380. Zbl 0501.20013.
^Allcock, Daniel (2005). "Orbits in the Leech Lattice". Experimental Mathematics. 14 (4). Taylor & Francis: 508. doi:10.1080/10586458.2005.10128938. MR 2193810. S2CID 2883584. Zbl 1152.11334.
"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."
^Wilson, Robert A. (1984). "On maximal subgroups of the Fischer group Fi22". Mathematical Proceedings of the Cambridge Philosophical Society. 95 (2): 197–222. doi:10.1017/S0305004100061491. ISSN 0305-0041. MR 0735364.
^Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Fischer group Fi22". ATLAS of Finite Group Representations.
^Nickerson, S.J.; Wilson, R.A. (2011). "Semi-Presentations for the Sporadic Simple Groups". Experimental Mathematics. 14 (3). Oxfordshire: Taylor & Francis: 359−371. doi:10.1080/10586458.2005.10128927. MR 2172713. S2CID 13100616. Zbl 1087.20025.
^ a bWilson, R.A (1998). "Chapter: An Atlas of Sporadic Group Representations" (PDF). The Atlas of Finite Groups - Ten Years On (LMS Lecture Note Series 249). Cambridge, U.K: Cambridge University Press. pp. 261–273. doi:10.1017/CBO9780511565830.024. ISBN 9780511565830. OCLC 726827806. S2CID 59394831. Zbl 0914.20016.
^Norton, S. P.; Wilson, Robert A. (1986). "Maximal subgroups of the Harada-Norton group". Journal of Algebra. 103 (1): 362–376. doi:10.1016/0021-8693(86)90192-4. ISSN 0021-8693. MR 0860712.
^Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Harada-Norton group HN". ATLAS of Finite Group Representations.
^ a bWilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". ATLAS of Finite Group Representations.
^Kleidman, Peter B.; Parker, Richard A.; Wilson, Robert A. (1989). "The maximal subgroups of the Fischer group Fi₂₃". Journal of the London Mathematical Society. Second Series. 39 (1): 89–101. doi:10.1112/jlms/s2-39.1.89. ISSN 0024-6107. MR 0989922.
^Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Fischer group Fi23". ATLAS of Finite Group Representations.
^Wilson, Robert A. (1999). "The maximal subgroups of the Baby Monster. I". Journal of Algebra. 211 (1): 1–14. doi:10.1006/jabr.1998.7601. MR 1656568.
^Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Baby Monster group B". ATLAS of Finite Group Representations.
^Drews (1972), p. 43, n. 10.
^Weinreich, Th., "Zwölfgötter", Ausführliches Lexikon der Griechischen und Römischen Mythologie, vol. VI, col. 764-848.
^"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.
^Attia, Peter (2018-09-05). "The Full History of Board Games". Medium. Retrieved 2020-10-22.
^"Shilling | currency". Encyclopedia Britannica. Retrieved 20 May 2021.
Sources
Collins, Billie Jean (2002), "Necromancy, Fertility and the Dark Earth: The Use of Ritual Pits in Hittite Cult", in Mirecki, Paul; Meyer, Marvin (eds.), Magic and Ritual in the Ancient World, Leiden, The Netherlands: Brill, pp. 224–233, ISBN 90-04-10406-2
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.
Journal articles
Poonen, Bjorn; Rodriguez-Villegas, Fernando (March 2000). "Lattice Polygons and the Number 12" (PDF). American Mathematical Monthly. 107 (3): 238–250. doi:10.1080/00029890.2000.12005186. S2CID 11433945. Archived from the original (PDF) on 2012-04-14.