This cusp form is the discriminant Δ( q) whose Fourier coefficients are given by the Ramanujan τ-function and which is (up to a constant multiplier) the 24th power of the Dedekind eta function. Twelve is the smallest weight for which a cusp form exists. Twelve is also the kissing number in three dimensions. The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. A twelve- faced polyhedron is a dodecahedron. If an odd perfect number is of the form 12 k + 1, it has at least twelve distinct prime factors.Ī twelve-sided polygon is a dodecagon. 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. 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. 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 also a highly composite number, the next one being twenty-four. Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12. The Duden (the German standard dictionary) mentions this rule as outdated. In German orthography, there used to be the widely followed (but unofficial) rule of spelling out numbers up to twelve ( zwölf).
Another system spells out all numbers written in one or two words ( sixteen, twenty-seven, fifteen thousand, but 372 or 15,001). 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. 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. Italian dodici (but in Spanish and Portuguese, 16, and in French, 17 is the first compound number), Japanese 十二 jūni.
It is a compound number in many other languages, e.g. Īs 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. The suffix * -lif- has also been connected with reconstructions of the Proto-Germanic for ten. The Lithuanian suffix is also considered to share a similar development. The adjective referring to a group of twelve is "duodecuple".Īs 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. Similarly, a group of twelve things is usually a " dozen" but may also be referred to as a "dodecad" or "duodecad". The usual ordinal form is "twelfth" but "dozenth" or "duodecimal" (from the Latin word) is also used in some contexts, particularly base-12 numeration. Every other Indo-European language instead uses a form of "two"+" ten", such as the Latin duōdecim. 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").
German zwölf), whose Proto-Germanic ancestor has been reconstructed as * twaliƀi., from * twa (" two") and suffix * -lif- or * -liƀ- of uncertain meaning. It has cognates in every Germanic language (e.g. Such uses gradually disappeared with the introduction of Arabic numerals during the 12th-century Renaissance.ĭerived from Old English, twelf and tuelf are first attested in the 10th-century Lindisfarne Gospels' Book of John. 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. Twelve is the largest number with a single-syllable name in English.
0 kommentar(er)
