12 (number)
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Bengali ১২ | | |||
Hebrew numeral | י"ב | |||
Babylonian numeral | 𒌋𒐖 |
12 (twelve) is the
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
Derived from
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 The Duden[year needed] (the German standard dictionary) mentions this rule as outdated.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
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,
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
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
A twelve-sided
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 -
in five-dimensional space.The Leech lattice, which holds the solution to the kissing number in twenty-four dimensions,[31] has a density equal to:
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
Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant whose Fourier coefficients are given by the
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
.In
In nature
Notably, twelve is the number of full
.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
- The
Judaism and Christianity
- The significance is especially pronounced in the Hebrew Bible.
- 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."
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.
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
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
- The chief Norse god, Odin, has twelve sons.[citation needed]
- In the King Arthur legend, Arthur is said to subdue 12 rebel princes and to win 12 great battles against Saxon invaders.[55]
- In sons of Jacob.
- In the mythologies of the ancient Hurrians and Hittites, there were the Twelve gods of the Underworld.
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 |
|
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
- The atomic number of magnesium in the periodic table.
- The Standard Model identifies twelve types of elementary fermions as well as twelve types of elementary gauge bosons.
- The human body has twelve cranial nerves.
- The Latin: duodecim, lit. 'twelve') is the first part of the small intestine, that is about twelve inches (30 cm) 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, in Dutch the name is twaalfvingerige darm and in Bulgarianthe name is дванадесетопръстник, all meaning "twelve-finger bowel".
- Force 12 on the Beaufort wind force scale corresponds to the maximum wind speed of a hurricane.
- The human body has twelve thoracic vertebrae.
- Messier 12 (NGC 6218), an globular cluster in the constellation Ophiuchus, located at 16,400 light years away from earth
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:
- 12
- 12 Angry Men (1957 and 1997)
- Cheaper by the Dozen
- Ocean's Twelve
- 12 Monkeys
- The Dirty Dozen
- The Twelve Chairs (1970, 1971 and 1976)
- 12 Rounds
- Twelve
- Twelve Years a Slave
Television
- The number twelve plays a significant role in the television franchise humanoid Cylons.
- Studio One
- "Number 12 Looks Just Like You" is an episode of the television show The Twilight Zone.
- Schoolhouse Rock! portrayed an alien child using base-twelvearithmetic in the short "Little Twelvetoes".
- 12 oz. Mouse was an animated television show on Adult Swim.
- The News 12 Networks are a group of American regional cable news television channels covering New York, New Jersey, and Connecticut.
- Les Douze Coups de Midi (douze = 12) is a French game show broadcast on TF1 with Jean-Luc Reichmann at midday CEST.
- In Star Twinkle PreCure, the Star Palace is home to the twelve Star Princesses, one for each sign of the Zodiac.
Theatre
- Twelfth Night is a comedy by William Shakespeare.
- The Vision of the Twelve Goddesses is a Jacobean masque by Samuel Daniel.
- Twelve Angry Men, by Reginald Rose, adapted from his own teleplay (see above).
Literature
- "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 Twelve Dancing Princesses is a folk tale.
- The epic poem by Virgilis 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.
- Miguel de Cervantes wrote twelve Novelas ejemplares.
- The number twelve is a key feature in the plot of the novel Murder on the Orient Express by Agatha Christie.
Music
Music theory
- Twelve is the 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.
- The twelve-tone technique (also dodecaphony) is a method of musical composition devised by Arnold Schoenberg. Music using the technique is called twelve-tone music.
- The twelve-bar blues is one of the most prominent chord progressions in popular music.
- 12-inch phonograph record.
Pop music
- The 12-inch singleis a vinyl record format.
- Twelfth Night is a progressive rock band.
- 12 Play is an R. Kelly album.
- The Number 12 Looks Like You is a mathcoreband.
- "12", a song from the album Brave Murder Day by Katatonia.
- 12 is a studio album by German singer Herbert Grönemeyer.
- Twelve is an album by Patti Smith.
- Twelve Deadly Cyns...and Then Some is an album by Cyndi Lauper.
- D12 a rap group also known as the Dirty Dozen.
- 12 Stones is an American Christian rock band.
- "12 Hundred" is a song by band Mushroomhead of their Savior Sorrow album.
- 12 is the 12th studio album by Keller Williams.
- "12" ("Dodeka" in Greek) is one of the most well-known hits by Anna Vissi.
- "Twelve drummers drumming" is the gift on the twelfth day of Christmas in the carol "The Twelve Days of Christmas".
- Twelve Girls Band are an all female Chinese musical group .
- 12 (American Song Book) is an album by Italian singer Mina.
- "Revelation #12" is a song by American rock band Marilyn Manson.
- 12 is the maximum score a competing entry can receive by each country in the Eurovision Song Contest.
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 Fightervideo 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
- There are 12 troy ounces in a troy pound (used for precious metals).
- Twelve of something is called a dozen.
- In the
- In Labours of Heracleswas increased from ten to make twelve.
- In English, twelve is the number of greatest magnitude that has just one syllable.
- 12 is the last number featured on the analogue clock, and also the starting point of the transition from A.M. to P.M. hours or vice-versa.
- There are twelve months within a year, with the last one being December.
- The level of grades in which one must attend school typically ends at 12 (although some jurisdictions may include a thirteenth grade depending on the country).[citation needed]
- Twelve hours form half a day, and twelve hours away from another lead to the same time but with a different period (ex. Twelve hours away from 6:00 AM leads to 6:00 PM).
- There are normally twelve pairs of ribs in the human body.
- The Twelve Tables or Leges Duodecim Tabularum, more informally simply Duodecim Tabulae, was the ancient legislation underlying Roman law.
- 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 Washington, D.C. courts. The number of jurors gave the title to the play (and subsequent films) Twelve Angry Men.
- Twelve men have walked on Earth's moon.
- The United States 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 Roswell UFO incidentand cover up future extraterrestrial contact.
- 12 is the number of the French department Aveyron.
- King Arthur's Round Table had 12 knights plus King Arthur himself.
- 12 foot.
- Alcoholics Anonymous has 12 steps, 12 traditions and 12 concepts for world service.
- Wilhelm Heinrich Schüßler developed a list of 12 biochemical cell salts, also known as tissue salts.
- In the People's Republic of China, 12 Core Socialist Valueswere promoted as part of a campaign beginning in 2012.
See also
Notes
- twelve" (an of ðæm tuelfum).[4]
References
- ^ 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.
- ^ Stevenson, W. H. (December 1899). "The Long Hundred and its Use in England". Archaeological Review. 4 (5): 313–317.
- S2CID 162146336.
- ^ John 6:71.
- ^ a b c d e f Oxford English Dictionary, 1st ed. "twelve, adj. and n." Oxford University Press (Oxford), 1916.
- ^ a b Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
- ^ Dantzig, Tobias (1930), Number: The Language of Science.
- ^ "Numbers: Writing Numbers // Purdue Writing Lab". Purdue Writing Lab. Retrieved 25 February 2020.
- ^ 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.
- ^ "Sloane's A000178: Superfactorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-07-29.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A001097 (Twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ "Sloane's A081357 : Sublime numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
- ^ Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
- Zbl 0657.10003.
- ^ Sloane, N. J. A. (ed.). "Sequence A002827 (Unitary perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-10.
- ^ 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.
- ^ 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.
- ^ 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.
- Zbl 1142.11086.
- ^ 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.
- S2CID 119730123.
- Zbl 0732.51002.
- Zbl 1100.30036.
- ^ 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.
- Zbl 1213.11144.
- Zbl 0501.20013.
- Zbl 1152.11334.
- "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."
- MR 0735364.
- ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Fischer group Fi22". ATLAS of Finite Group Representations.
- Zbl 1087.20025.
- ^ Zbl 0914.20016.
- Zbl 1089.20006.
- ^ 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.
- MR 0860712.
- ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Harada-Norton group HN". ATLAS of Finite Group Representations.
- ^ a b Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". ATLAS of Finite Group Representations.
- MR 0989922.
- ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Fischer group Fi23". ATLAS of Finite Group Representations.
- MR 1656568.
- ^ Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Baby Monster group B". ATLAS of Finite Group Representations.
- ^ Drews (1972), p. 43, n. 10.
- ^ Weinreich, Th., "Zwölfgötter", Ausführliches Lexikon der Griechischen und Römischen Mythologie, vol. VI, col. 764-848.
- ^ "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.
- ^ "Surah Al-Baqarah - 60". Quran.com. Retrieved 2023-08-02.
- ^ "Surah Al-A'raf - 160". Quran.com. Retrieved 2023-08-02.
- ^ "Surah At-Tawbah - 36". Quran.com. Retrieved 2023-08-02.
- ^ Collins 2002, p. 228.
- ^ Benet's Reader's Encyclopedia, 3d ed.
- ^ "Lunar versus solar calendar".
- ^ Attia, Peter (2018-09-05). "The Full History of Board Games". Medium. Retrieved 2020-10-22.
- ^ "Shilling | currency". Encyclopedia Britannica. Retrieved 20 May 2021.
Sources
- Collins, Billie Jean (2002), "Necromancy, Fertility and the Dark Earth: The Use of Ritual Pits in Hittite Cult", in Mirecki, Paul; Meyer, Marvin (eds.), Magic and Ritual in the Ancient World, Leiden, The Netherlands: Brill, pp. 224–233, ISBN 90-04-10406-2
- JSTOR 292899..
Further reading
Books
- 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.
Journal articles
- Poonen, Bjorn; Rodriguez-Villegas, Fernando (March 2000). "Lattice Polygons and the Number 12" (PDF). American Mathematical Monthly. 107 (3): 238–250. S2CID 11433945. Archived from the original(PDF) on 2012-04-14.
External links
- Media related to 12 (number) at Wikimedia Commons