12 (number)

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12
Cardinal twelve
Ordinal 12th
(twelfth)
Numeral system duodecimal
Factorization 2^2 \cdot 3
Divisors 1, 2, 3, 4, 6, 12
Roman numeral XII
Binary 1100
Octal 14
Duodecimal 10
Hexadecimal C
Mathematical properties
φ(12) = 4 τ(12) = 6
σ(12) = 28 π(12) = 5
μ(12) = 0 M(12) = -2
Look up twelve in
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12 (twelve) is the natural number following 11 and preceding 13.

The word "twelve" is a native English word that presumably arises from the Germanic compound twa-lif "two-leave", meaning that two is left before one takes away the base, ten. This compound meaning may have been transparent to speakers of Old English, but the modern form "twelve" is quite translucent. Only the remaining tw- hints that twelve and two are related. Etymology (Weekley, Skeat) suggests that "twelve" (similar to "eleven") consists of two parts, the first meaning "two" and the second "leftover", so a literal translation would yield "two remaining [after having ten taken]".

A group of twelve things is called a Duodecad. The ordinal adjective is duodenary, twelfth. The adjective referring to a group consisting of twelve things is duodecuple.

The number twelve is often used as a sales unit in trade, and is often referred to as a dozen. Twelve dozen are known as a gross. (Note that there are thirteen items in a baker's dozen.)

As shown below, the number twelve is frequently referenced in the Abrahamic religions and is also central to Western calendar and units of time.

Contents

[edit] In mathematics

  • It is the first composite number of the form p2q; a square prime, and also the first member of the (p2) family in this form.
  • Twelve is a superfactorial, being the product of the first three factorials.
  • Twelve being the product of three and four, the first four positive integers show up in the equation 12 = 3 × 4, which can be continued with the equation 56 = 7 × 8.
  • 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). Twelve is also the kissing number in three dimensions.
  • In base thirteen and higher bases (such as hexadecimal), twelve is represented as C.
  • Twelve is the ninth Perrin number, preceded in the sequence by 5, 7, 10.
  • 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 τ-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 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.
  • 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.

There are twelve Jacobian elliptic functions.

[edit] List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 50 100 1000
12 \times x 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 300 600 1200 12000

[edit] In numeral systems

١٢ Arabic ԺԲ Armenian
ιβ´ Ionian Greek ΔΙΙ Attic Greek
יב Hebrew
V20 Z1 Z1
Egyptian
१२ Indian (Devanāgarī) 十二 Chinese and Japanese
௧௨ Tamil Ⅻ Roman and Etruscan
๑๒ Thai IIX Chuvash



[edit] In science

Magnesium dioxide dissovles at 12oc

[edit] Astronomy

[edit] In religion

Religion inherits the number twelve for its magical properties.

[edit] In time

  • Most calendar systems have twelve months in a year.
  • The Western zodiac has twelve signs, as does the Chinese zodiac.
  • The Chinese use a 12 years cycle for time-reckoning called Earthly Branches.
  • There are twenty-four hours in a day in all, with twelve hours for a half a day. The hours are numbered from one to twelve for both the ante meridiem (a.m.) half of the day and the post meridiem (p.m.) half of the day. 12:00 after a.m. and before p.m. (in the middle of the day) is midday or noon, and 12:00 after p.m. and before a.m. (in the middle of the night) is midnight. A new day is considered to start with the stroke of midnight. Furthermore, the basic units of time (60 seconds, 60 minutes, 24 hours) can all perfectly divide by twelve.
  • The minute hand of a clock face turns twelve times as fast as the hour hand.

[edit] In sports

[edit] In technology

[edit] In the arts

[edit] Film

Movies with the number twelve or its variations in their titles include

[edit] Television

[edit] Theatre

[edit] Literature

[edit] Music

[edit] Art Theory

  • 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).

[edit] Games

  • The Roman form of 12 (XII) is used as the symbol of the organization MJ12 in the Deus Ex computer game.

[edit] In other fields

  • There are 12 in a dozen.
  • There are 12 ounces in a troy pound (used for precious metals), and 12 constellations in the ecliptic (or signs of the zodiac).
  • In the former British currency system, there were twelve pence in a shilling.
  • In astrology, there are 12 signs in the Zodiac.
  • In Greek mythology, the number of labours of Heracles was increased from ten to make twelve.
  • The number of dan (master) grades in judo.
  • 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.
  • Twelve stars are featured on the European flag.
  • The car number of NASCAR's Ryan Newman.
  • 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 D.C. courts. The number of jurors gave the title to the play (and subsequent films) 12 Angry Men.
  • Twelve men have walked on the 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.

[edit] Historical years

12 A.D., 12 B.C., 1912, 2012, etc.

[edit] See also

[edit] Notes

  1. ^ The classic assembly of instances is Th. Weinreich, "Zwölfgötten' in W.H. Roscher, Ausfurliches Lexikon der Griechischen und Römishen Mythologie vol. vi. col. 764-848, noted in Robert Drews, "Light from Anatolia on the Roman Fasces"The American Journal of Philology 93.1 (January 1972) pp. 40-51) p 43 note 10. The twelve lictors carried fasces of twelve rods.

[edit] References

 This article needs additional citations for verification.
Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (March 2008)
  • 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. 
  • Lattice Polygons and the Number 12, Bjorn Poonen, Fernando Rodriguez-Villegas, American Mathematical Monthly, Vol. 107, No. 3 (Mar., 2000) , pp. 238-250 [1]

[edit] External links