12 (number)

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Cardinal 12
twelve
Ordinal 12th
twelfth
Numeral system duodecimal
Factorization <math>2^2 \cdot 3</math>
Divisors 1, 2, 3, 4, 6, 12
Roman numeral XII
Unicode representation of Roman numeral Ⅻ, 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

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 after 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 opaque. 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.

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 loaves in a baker's dozen.)

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In mathematics

  • The duodecimal system (1210 [twelve] = 1012), which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia. As Schoolhouse Rock explains in its song "Little Twelvetoes", if humankind had been born with twelve fingers, they would have counted and multiplied using the duodecimal system. (There is no need to have twelve fingers though, since one will easily arrive at the duodecimal system by simply counting the phalanx bones of fingers with the same hand's thumb, a practice in use with some people until the present day.)
  • 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.
  • In base thirteen and higher bases (such as hexadecimal), twelve is represented as C.
  • 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.
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Geometry

Image:Dodecahedron.jpg Image:Rhombicdodecahedron.jpg It is possible to construct a perfect circle divided into twelve sectors of 30 degrees each, using only a compass and straightedge.

  1. Using a compass, construct a simple circle.
  2. Taking care not to change the radius setting, draw a second circle with center anywhere on the perimeter of the first.
  3. Now go to the two points where the second circle crosses the first, and draw two more circles from these centers.
  4. Continue this process to draw the final three circles, working your way around the perimeter of the first.
  5. Finally connect the center of the original circle with all other points of intersection, using a straightedge.
You now have twelve radial lines emanating from the center, separated by twelve 30-degree sectors, all constructed from seven equal-sized circles.
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In numeral systems

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Template:Lang Hebrew <hiero>V20-Z1-Z1</hiero> Egyptian
Template:Lang Indian (Devanāgarī) Template:Lang Chinese character
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In science

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Astronomy

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In time

  • There are twelve months in a year.
  • The Western zodiac has twelve signs, as does the Chinese zodiac.
  • The Chinese use a 12 year 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 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.
  • The minute hand of a clock face turns twelve times as fast as the hour hand.
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In religion

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In music

  • 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.
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In sports

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In technology

  • ASCII and Unicode code point for form feed.
  • The number of function keys on most PC keyboards (F1 through F12)
  • The number of dialling keys in any standard digital telephone (1 through 9, 0, * and #)
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In the arts

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Film

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

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Theater

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Music

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Games

  • Twelve is a character in the Street Fighter video game
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Other

  • There are 12 ounces in a troy pound (used for precious metals), and 12 constellations in the ecliptic (or signs of the zodiac),
  • In Greek mythology, the number of labours of Heracles (Hercules).
  • 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.
  • 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 in the movie gave the title to the film 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.
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See also

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References

  • Template:Cite book
  • Lattice Polygons and the Number 12, Bjorn Poonen, Fernando Rodriguez-Villegas, American Mathematical Monthly, Vol. 107, No. 3 (Mar., 2000) , pp. 238-250 [1]
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External links

ca:Dotze da:12 (tal) de:Zwölf es:Doce eo:Dek du fr:12 (nombre) ko:12 it:Dodici he:12 (מספר) la:12 lt:12 (skaičius) nah:Mahtlahtlinome nap:Dùrece nl:12 (getal) ja:12 no:12 (tall) nn:Talet 12 pl:12 (liczba) pt:Doze ru:12 (число) simple:Twelve sl:12 (število) sv:12 (tal) zh:12

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