Derived from Old English, twelf and tuelf are first attested in the 10th-century Lindisfarne Gospels' Book of John.[note 1] 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. It is sometimes compared with the Lithuaniandvýlika, although -lika is used as the suffix for all numbers from 11 to 19 (analogous to "-teen"). Every other Indo-European language instead uses a form of "two"+"ten", such as the Latinduōdecim. 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, 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. The Lithuanian suffix is also considered to share a similar development. The suffix *-lif- has also been connected with reconstructions of the Proto-Germanic for ten.
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]
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).
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 The Duden[year needed] (the German standard dictionary) mentions this rule as outdated.
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. 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 the smallest weight for which a cusp form exists. This cusp form is the discriminant Δ(q) whose Fourier coefficients are given by the Ramanujanτ-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 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.
12 is the negative reciprocal of the Ramanujan summation of the infinite series 1 + 2 + 3 + 4 + ⋯. Although the series is divergent, methods such as Ramanujan summation can assign finite values to divergent series.
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, in Dutch the name is twaalfvingerige darm and in Bulgarian the name is дванадесетопръстник, all meaning "twelve-finger bowel".
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.
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).
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.
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.
^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.
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.
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.