Twelve and Duodecad (K-12)!

The word “twelve” is the largest number with a single-morpheme name in English. Etymology suggests that “twelve” (similar to “eleven”) arises from the Germanic compound twalif “two-leftover”, so a literal translation would yield “two remaining [after having ten taken]”.

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. 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 cited in the Abrahamic religions and is also central to Western calendar and units of time.

IN MATHEMATICS

Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12. Twelve is also a highly composite number, the next one being 24. 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. 12 has an aliquot sum of 16 (133% in abundance). Accordingly, 12 is the first abundant number (in fact a superabundant number) and demonstrates an 8 member aliquot sequence; {12,16,15,9,4,3,1,0} 12 is the 3rd composite number in the 3-aliquot tree.

The only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant (18 and 20). 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 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. Twelve is the ninth Perrin number, preceded in the sequence by 5, 7, 10, and also appears in the Padovan sequence, preceded by the terms 5, 7, 9 (it is the sum of the first two of these). It is the fourth Pell number, preceded in the sequence by 2 and 5 (it is the sum of the former plus twice the latter).

A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. 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. 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. There are twelve Jacobian elliptic functions and twelve cubic distance-transitive graphs.

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. In base thirteen and higher bases (such as hexadecimal), twelve is represented as C. In base 10, the number 12 is a Harshad number.

IN EXPONENTIATION

1             2              3                4                       5
12         144          1728           20736             248832

 

IN SCIENCE

• The atomic number of magnesium in the periodic table.

• The human body has twelve cranial nerves.

• The duodenum (from Latin duodecim, “twelve”) is the first part of the small intestine, that is about twelve inches 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 and in Dutch the name is twaalfvingerige darm, both meaning “twelve-finger bowel.”

• Force 12 on the Beaufort wind force scale corresponds to the maximum wind speed of a hurricane.

 

IN ASTRONOMY

• Messier object M12, a magnitude 8.0 globular cluster in the constellation Ophiuchus

• The New General Catalogue object NGC 12, a magnitude 13.1 spiral galaxy in the constellation Pisces

• The Saros number of the solar eclipse series which began on 2680 BC BC August and ended on 1129 BC BC February. The duration of Saros series 12 was 1550.5 years, and it contained 87 solar eclipses.

• The Saros number of the lunar eclipse series which began on 2360 BC BC May and ended on 1062 BC BC July. The duration of Saros series 12 was 1298.1 years, and it contained 73 lunar eclipses.

• The 12th moon of Jupiter is Lysithea.

 

IN RELIGION

There are twelve ‘ Jyotirlingas’ (epitome of God Shiva) in Hindu Shaivism. The shaivites (orthodox devotees of God Shiva) treat them with great respect and these are visited by almost every pious Hindu at least once in a lifetime.

The number 12 is very important in many religions, mainly Judaism, Christianity, and Islam, and also found in some older religions and belief systems. In Antiquity there are numerous magical/religious uses of twelves.

Ancient Greek religion, the Twelve Olympians were the principal gods of the pantheon. The chief Norse god, Odin, had 12 sons. Several sets of twelve cities are identified in history as a dodecapolis, the most familiar being the Etruscan League. In the King Arthur Legend, Arthur is said to have subdued 12 rebel princes and to have won 12 great battles against Saxon invaders.

The importance of 12 in Judaism and Christianity can be found in the Bible. The biblical Jacob had 12 sons, who were the progenitors of the Twelve Tribes of Israel, while the New Testament describes twelve apostles of Jesus; when Judas Iscariot was disgraced, a meeting was held (Acts) to add Matthias to complete the number twelve once more. (Today, The Church of Jesus Christ of Latter-day Saints has a Quorum of the Twelve Apostles).

The Book of Revelation contains much numerical symbolism, and a lot of the numbers mentioned have 12 as a divisor. 12:1 mentions a woman — interpreted as the people of Israel, the Church or 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, making a total of 144,000 (which is the square of 12 multiplied by a thousand).

In Orthodox Judaism, 12 signifies the age a girl matures (bat mitzvah) There are 12 days of Christmas. The song Twelve Days of Christmas came from the traditional practice of extending Yuletide celebrations over the twelve days from Christmas day to the eve of Epiphany; the period of thirteen days including Epiphany is sometimes known as Christmastide. Thus Twelfth Night is another name for the twelfth day of Christmas or January 5 (the eve of Epiphany). Similarly, Eastern Orthodoxy observes 12 Great Feasts.

In Shi’a Islam, there are twelve Imams, legitimate successors of the prophet Muhammad. These twelve early leaders of Islam are—Ali, Hasan, Husayn, and nine of Husayn’s descendants. Imāmah (Arabic: إمامة‎) is the Shī‘ah doctrine of religious, spiritual and political leadership of the Ummah. The Shī‘ah believe that the A’immah (“Imams”) are the true Caliphs or rightful successors of Muḥammad, and Twelver and Ismā‘īlī Shī‘ah further that Imams are possessed of supernatural knowledge, authority, and infallibility (‘Iṣmah) as well as being part of the Ahl al-Bayt, the family of Muhammad. Both beliefs distinguish the Shī‘ah from Sunnis.

In Hinduism, the sun god Surya has 12 names. Also, there are 12 Petals in Anahata(Heart Chakra.)

 

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 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 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. The basic units of time (60 seconds, 60 minutes, 24 hours) can all perfectly divide by twelve.

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 keys in any standard digital telephone (1 through 9, 0, * and #) • Microsoft’s Rich Text Format specification assigns numbers congruent to 12 mod 256 to variants of the French language.

 

IN LITERATURE

• The Twelve is a poem by Aleksandr Blok

• Twelve is a novel by Nick McDonell • The Twelve Chairs is a satirical novel by the Soviet authors Ilf and Petrov

• Cheaper by the Dozen is a 1946 novel by Frank Bunker Gilbreth, Jr. and Ernestine Gilbreth Carey

• The Aeneid, an epic poem by Virgil is divided into two halves composed of twelve books.

• Paradise Lost, an epic poem by John Milton is divided into twelve books perhaps in imitation of the Aeneid

IN 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).

 

source:http://en.wikipedia.org/wiki/12_(28number)

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