12 (number)

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Bengali
১২
Hebrew numeralי"ב
Babylonian numeral𒌋𒐖

12 (twelve) is the

6
.

It is the number of years required for an orbital period of Jupiter. It is central to many systems of timekeeping, including the Western calendar and units of time of day and frequently appears in the world's major religions.

Name

Twelve is the largest number with a

12th-century Renaissance
.

Derived from

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,[6] 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.[5] The Lithuanian suffix is also considered to share a similar development.[5] The suffix *-lif- has also been connected with reconstructions of the Proto-Germanic for ten.[6][7]

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 ] Japanese 十二 jūni.[clarification needed]

Written representation

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).[8] 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 The Duden[year needed] (the German standard dictionary) mentions this rule as outdated.

Mathematical properties

12 is the sixth

4, 6 and 12) which makes it the fifth highly composite number,[15] and since 6 is also one of them, twelve is also the fifth refactorable number.[16] 12, as a number with a perfect number of divisors (six), has a sum of divisors that yields the second perfect number, σ(12) = 28,[17] and as such it is the smallest of two known sublime numbers, which are numbers that have a perfect number of divisors whose sum is also perfect.[18] 12 is the fifth Pell number (preceded by 0, 1, 2, and 5)[19] as well as the third pentagonal number,[20] and a Harshad number in all bases except octal
.

Twelve is the number of divisors of 60 and 90, the second and third unitary perfect numbers (6 is the first). It is also the number of distinct prime factors that belong to the fifth unitary perfect number, the largest known,

[21][22]

The second perfect number, 28, is the arithmetic mean of the twelve divisors of the fourth harmonic divisor number, 140 (like 6, and 28), which generates an integer harmonic mean of 5.[23][24][25]

If an odd

prime factors.[26]

There are 12 Latin squares of size 3 × 3, where symbols appear exactly once in each row and exactly once in each column.[27]

There are twelve

Jacobian elliptic functions and twelve cubic distance-transitive graphs
.

A twelve-sided

snub hexagonal tiling are counted separately.[28]

A regular

.

The densest three-dimensional lattice sphere packing has each sphere touching twelve other spheres, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Twelve is also the kissing number in three dimensions.

There are twelve complex apeirotopes in dimensions five and higher, which include van Oss polytopes in the form of complex -

orthoplexes.[29] There are also twelve paracompact hyperbolic Coxeter groups of uniform polytopes
in five-dimensional space.

is equal to .

The Leech lattice, which holds the solution to the kissing number in twenty-four dimensions,[31] has a density equal to:

[32]

Its quaternionic representation contains vectors modulo that are congruent to either one of coordinate-frames, or zero;[33][34] with 1,365 the twelfth Jacobsthal number, and 144 equal to 122.

Fischer group is a sporadic group with a total of twelve maximal subgroups, the smallest of which is Mathieu group .[35][36] holds standard generators equal to (2A, 13, 11),[37] with a further condition where .[38] Furthermore, its faithful complex representation is 78-dimensional,[39] where 78 is the twelfth triangular number.[40] Otherwise, the largest alternating group represented inside any sporadic groups is , as a maximal subgroup inside the third-largest

Harada-Norton group
.[41][42] While or are not maximal subgroups of the largest sporadic group, the friendly giant , one of its maximal subgroup is .
double cover
is a maximal subgroup of ,[44][45] which is the third-largest maximal subgroup inside ;[46][47] with the double cover as the largest maximal subgroup inside .[43] The smallest second generation sporadic group, Janko group , holds standard generators (2A, 3B, 7) that yield .[38]

Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant whose Fourier coefficients are given by the

Ramanujan
-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 fact that the abelianization of special linear group has twelve elements, to the value of the Riemann zeta function at being , which stems from the Ramanujan summation

Although the series is divergent, methods such as Ramanujan summation can assign finite values to divergent series.

  • 12 is an Anti-Meertens Number. If we power the digits from the end to the prime numbers starting from 2 and then multiply, then the result will be the number Itself.

2^2 * 3^1 = 12

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 23 24 25 50 100 1000
12 × x 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 600 1200 12000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
12 ÷ x 12 6 4 3 2.4 2 1.714285 1.5 1.3 1.2 1.09 1 0.923076 0.857142 0.8 0.75
x ÷ 12 0.083 0.16 0.25 0.3 0.416 0.5 0.583 0.6 0.75 0.83 0.916 1 1.083 1.16 1.25 1.3
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12
12x 12 144 1728 20736 248832 2985984 35831808 429981696 5159780352 61917364224 743008370688 8916100448256
x12 1 4096 531441 16777216 244140625 2176782336 13841287201 68719476736 282429536481 1000000000000 3138428376721 8916100448256

In other bases

The

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 nature

Notably, twelve is the number of full

Islamic and the Chinese zodiac. Twelve is also the number of years for an orbital period of Jupiter
.

Religion

The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.[48]

Ancient Greek religion

Judaism and Christianity

Saint Matthias
to complete the number twelve once more. The
144,000
(which is the square of 12 multiplied by a thousand).

  • According to the New Testament, Jesus had
    twelve Apostles
    .
  • The "
    Epiphany
    .
  • Eastern Orthodoxy observes twelve
    Great Feasts
    .

12 was the only number considered to be religiously divine in the 1600s causing many Catholics to wear 12 buttons to church every Sunday. Some extremely devout Catholics would always wear this number of buttons to any occasion on any type of clothing.[citation needed]

Islam

Twelve is referred to in three different verses of the Quran. Two are in reference to the Twelve Tribes of Israel.

And ˹remember˺ when Moses prayed for water for his people, We said, "Strike the rock with your staff." Then twelve springs gushed out, ˹and˺ each tribe knew its drinking place. ˹We then said,˺ "Eat and drink of Allah’s provisions, and do not go about spreading corruption in the land."

— Surah Al-Baqarah (The Heifer):60[51]

The second reference is:

We divided them into twelve tribes—each as a community. And We revealed to Moses, when his people asked for water, "Strike the rock with your staff." Then twelve springs gushed out. Each tribe knew its drinking place. We shaded them with clouds and sent down to them manna and quails,1 ˹saying˺, "Eat from the good things We have provided for you." They ˹certainly˺ did not wrong Us, but wronged themselves.

— Surah Al-A'raf (The Heights):160[52]

Note 1: Manna (heavenly bread) and quails (chicken-like birds) sustained the children of Israel in the wilderness after they left Egypt.

The last reference is to the number of months and the sacred ones amongst them:

Indeed, the number of months with Allāh is twelve [lunar] months in the register of Allāh [from] the day He created the heavens and the earth; of these, four are sacred.2

— Surah At-Tawbah (The Repentance):36[53]

Note 2: The four sacred months of the Islamic calendar are Dhu al-Qa'dah, Dhu al-Hijjah, Muharram, and Rajab (months 11, 12, 1 and 7).

Hinduism

  • There are twelve Jyotirlinga (Self-formed Lingas) of Lord Shiva in Hindu temples across India according to the Shaiva tradition.
  • The Sun god Surya has 12 names.
  • The god Hanuman has 12 names.
  • There are 12 Petals in Anahata or "heart chakra".
  • There are frequently said to be 12
    Âdityas
    .

Others

Ancient Hittite relief carving from Yazılıkaya, a sanctuary at Hattusa, depicting twelve gods of the underworld[54]

Law

  • The number of twelve jurors in jury trials is depicted by Aeschylus in the Eumenides. In the play, the innovation is brought about by the goddess Athena, who summons twelve citizens to sit as jury.
  • In English Common Law, the tradition of twelve jurors harks back to the 10th-century law code introduced by
    Aethelred the Unready
    .

Timekeeping

  • The
    solar year.[56]
  • Most calendar systems – solar or lunar – have twelve months in a year.
  • The Chinese use a 12-year cycle for time-reckoning called Earthly Branches.
  • There are twelve hours in a half day, numbered one to twelve for both the ante meridiem (a.m.) and the post meridiem (p.m.). 12:00 p.m. is midday or noon, and 12:00 a.m. is midnight.
  • The basic units of time (60 seconds, 60 minutes, 24 hours) are evenly divisible by twelve into smaller units.

In numeral systems

۱۲ Arabic ១២ Khmer ԺԲ Armenian
১২
Bangla
ΔΙΙ Attic Greek 𝋬 Maya
יב Hebrew
V20Z1Z1
Egyptian
१२
Devanāgarī
)
十二 Chinese and Japanese
௧௨ Tamil XII Roman and Etruscan
๑๒ Thai IIX Chuvash
౧౨ Telugu and Kannada ١٢
Urdu
ιβʹ Ionian Greek ൧൨ Malayalam

In science

Image of the globular cluster Messier 12 by Hubble Space Telescope

In sports

  • In both
    Cork City do not allow field players to wear the number 12 on their jersey because it is reserved for their supporters. It also serves as the jersey number for some the National Football League's best and most well-known quarterback, Tom Brady
    .
  • In Canadian football, 12 is the maximum number of players that can be on the field of play for each team at any time.
  • In cricket, another sport with eleven players per team, teams may select a "12th man", who may replace an injured player for the purpose of fielding (but not batting or bowling).
  • In women's lacrosse, each team has 12 players on the field at any given time, except in penalty situations.
  • In rugby league, one of the starting second-row forwards wears the number 12 jersey in most competitions. An exception is in the Super League, which uses static squad numbering.
  • In rugby union, one of the starting centres, most often but not always the inside centre, wears the 12 shirt.
  • In an NBA game, a quarter lasts 12 minutes.
  • In pool:
    • The pool ball 12 is the 12th in pool and its color is purple.

In technology

  • 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 the arts

Film

Films with the number twelve or its variations in their titles include:

Television

Theatre

Literature

Music

Music theory

Pop music

Art theory

  • 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).

Games

  • 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.
  • Twelve is a character in the Street Fighter
    video game series.
  • Games such as Backgammon have a long history of 12 points on each side of the gaming board, as evidenced in the XII scripta board in the museum at Ephesus.[57]

In other fields

12 stars are featured on the Flag of Europe.

See also

Notes

  1. twelve" (an of ðæm tuelfum).[4]

References

  1. ^ Gordon, E. V. (1957). Introduction to Old Norse. Oxford, England: Clarendon Press. pp. 292–293. Archived from the original on 2016-04-15. Retrieved 2017-09-08.
  2. ^ Stevenson, W. H. (December 1899). "The Long Hundred and its Use in England". Archaeological Review. 4 (5): 313–317.
  3. S2CID 162146336
    .
  4. ^ John 6:71.
  5. ^ a b c d e f Oxford English Dictionary, 1st ed. "twelve, adj. and n." Oxford University Press (Oxford), 1916.
  6. ^ a b Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
  7. ^ Dantzig, Tobias (1930), Number: The Language of Science.
  8. ^ "Numbers: Writing Numbers // Purdue Writing Lab". Purdue Writing Lab. Retrieved 25 February 2020.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  10. ^ "Sloane's A000178: Superfactorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-29.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A005835 (Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  14. ^ Sloane, N. J. A. (ed.). "Sequence A001097 (Twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers, definition (1): numbers n where d(n), the number of divisors of n (A000005), increases to a record.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-19.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  18. ^ "Sloane's A081357 : Sublime numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  21. .
  22. ^ Sloane, N. J. A. (ed.). "Sequence A002827 (Unitary perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A000203 (Sigma n, the sum of the divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers: numbers n such that the harmonic mean of the divisors of n is an integer.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A001600 (Harmonic means of divisors of harmonic numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-11.
  26. .
  27. ^ Sloane, N. J. A. (ed.). "Sequence A002860 (Number of Latin squares of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-19.
  28. S2CID 119730123
    .
  29. .
  30. .
  31. ^ Sloane, N. J. A. (ed.). "Sequence A002336 (Maximal kissing number of n-dimensional laminated lattice.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-06.
    Equal to 196,560 24-spheres in twenty-four dimensions.
  32. .
  33. .
  34. .
    "The reader should note that each of Wilson's frames [Wilson 82] contains three of ours, with 3 · 48 = 144 vectors, and has slightly larger stabilizer."
  35. .
  36. ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Fischer group Fi22". ATLAS of Finite Group Representations.
  37. .
  38. ^ .
  39. .
  40. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) is binomial(n+1,2) equal to n*(n+1)/2, in-turn 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-07-31.
  41. .
  42. ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Harada-Norton group HN". ATLAS of Finite Group Representations.
  43. ^ a b Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". ATLAS of Finite Group Representations.
  44. .
  45. ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Fischer group Fi23". ATLAS of Finite Group Representations.
  46. .
  47. ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Baby Monster group B". ATLAS of Finite Group Representations.
  48. ^ Drews (1972), p. 43, n. 10.
  49. ^ Weinreich, Th., "Zwölfgötter", Ausführliches Lexikon der Griechischen und Römischen Mythologie, vol. VI, col. 764-848.
  50. ^ "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.
  51. ^ "Surah Al-Baqarah - 60". Quran.com. Retrieved 2023-08-02.
  52. ^ "Surah Al-A'raf - 160". Quran.com. Retrieved 2023-08-02.
  53. ^ "Surah At-Tawbah - 36". Quran.com. Retrieved 2023-08-02.
  54. ^ Collins 2002, p. 228.
  55. ^ Benet's Reader's Encyclopedia, 3d ed.
  56. ^ "Lunar versus solar calendar".
  57. ^ Attia, Peter (2018-09-05). "The Full History of Board Games". Medium. Retrieved 2020-10-22.
  58. ^ "Shilling | currency". Encyclopedia Britannica. Retrieved 20 May 2021.

Sources

Further reading

Books

Journal articles

External links