42 (number)
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42 | |
---|---|
Cardinal | forty-two |
Ordinal | 42nd (forty-second) |
Factorization | 2 · 3 · 7 |
Divisors | 1, 2, 3, 6, 7, 14, 21, 42 |
Roman numeral | XLII |
Binary | 1010102 |
Octal | 528 |
Duodecimal | 3612 |
Hexadecimal | 2A16 |
42 (forty-two) is the natural number following 41 and preceding 43.
Contents |
[edit] In mathematics
Forty-two is an abundant number; its factorization 2 · 3 · 7 makes it the second sphenic number and also the second of the form { 2 · 3 · r }. As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed by twin primes; 30 also rests between two primes. 42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30. Further, 42 is the 10th member of the 3-aliquot tree.
42 is the product of the first three terms of Sylvester's sequence; like the first four such numbers it is also a primary pseudoperfect number.
It is the sum of the totient function for the first eleven integers.
It is a Catalan number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
It is the reciprocal of a Bernoulli number.
It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function". In particular, Conrey & Ghosh have conjectured
where the infinite product is over all prime numbers, p.[1][2]
It is a pronic number, and the third 15-gonal number. It is a meandric number and an open meandric number.
Since the greatest prime factor of 422 + 1 = 1765 is 353 and thus more than 42 twice, 42 is a Størmer number.
42 is a perfect score on the USA Math Olympiad (USAMO)[3] and International Mathematical Olympiad (IMO).[4]
In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).
The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3×3×3 "magic cube" can be constructed such that every row, column, and corridor, and every diagonal passing through the center, comprises 3 cubes whose sum of values is 42.
[edit] In science
- The atomic number of molybdenum.
- The angle in degrees for which a rainbow appears.
- In 1965, mathematician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the Earth, connecting a set of antipodes, evacuate it (remove the air), and then just fall through. The first half of the journey consists of free-fall acceleration, while the second half consists of an exactly equal deceleration. The time for such a journey works out to be 42 minutes. Remarkably, even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity always works out to be 42 minutes, as long as the tube remains friction-free, as while gravity's force would be lessened, so would the distance traveled at an equal rate.[5][6] The same idea was proposed by Lewis Carroll in Sylvie and Bruno, volume 2, chapter 7, without calculation.
[edit] In astronomy
- Messier object M42, a magnitude 5.0 diffuse nebula in the constellation Orion, also known as the Orion Nebula
- The New General Catalogue object NGC 42, a spiral galaxy in the constellation Pegasus
- In January 2005, Asteroid 2001 DA42 was given the name Asteroid Douglasadams, named for the author Douglas Adams who popularized the number 42 and died in 2001. With even his initials in the provisional designation, Brian G. Marsden, the director of the Minor Planet Center and the secretary for the naming committee, said, "This was sort of made for him, wasn't it?"
[edit] In religion
The number 42 appears in various contexts in Christianity. There are 42 generations (names) in the Gospel of Matthew's version of the Genealogy of Jesus; it is prophesied that for 42 months the Beast will hold dominion over the Earth (Revelation 13:5); 42 men of Beth-azmaveth were counted in the census of men of Israel upon return from exile (Ezra 2:24); God sent bears to maul 42 of the youths who mock Elisha for his baldness (2 Kings 2:23), etc.
42 also occurs in other religions. There are 42 principles of Ma'at, the Ancient Egyptian personification of physical and moral law, order, and truth. In the judgement scene described in the Egyptian and the Book of the Coming/Going Forth by Day (the Book of the Dead (which evolved from the Coffin Texts and the Pyramid Texts)), there are 42 Gods and Goddesses of Egypt, personifying the principles of Ma'at, who ask questions of the departed, while Thoth records the answers, and the deceased's heart is weighed against the feather of Truth (Ma'at). These 42 correspond to the 42 Nomes (Governmental Units) of Egypt. If the departed successfully answers all 42, s/he becomes an Osiris.
In Judaism, the number (in the Babylonian Talmud, compiled 375 AD to 499 AD) of the "Forty-Two Lettered Name" ascribed to God. Rab (or Rabhs), a 3rd century source in the Talmud stated "The Forty-Two Lettered Name is entrusted only to him who is pious, meek, middle-aged, free from bad temper, sober, and not insistent on his rights". [Source: Talmud Kidduschin 71a, Translated by Rabbi Dr. I. Epstein]. Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names [Maimonides "Moreh"]. The apparently unpronouncable Tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Two Lettered Name of the Talmud.
42 is the number with which God creates the Universe in Kabalistic tradition. In Kabbalah, the most significant name is that of the En Sof (also known as "Ein Sof", "Infinite" or "Endless"), who is above the Sefirot (sometimes spelled "Sephirot").[7] The Forty-Two-Lettered Name contains four combined names which are spelled in Hebrew letters (spelled in letters = 42 letters), which is the name of Azilut (or "Atziluth" "Animation"). While there are obvious links between the Forty-Two Lettered Name of the Babylonian Talmud (see further up this page) and the Kabbalah's Forty-Two Lettered Name, they are probably not identical due to the Kabbalah's emphasis on numbers. The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.
[edit] In popular culture
[edit] In The Hitchhiker's Guide to the Galaxy
Many occurrences of the number 42 in pop culture can be attributed as an homage to Douglas Adams' book The Hitchhiker's Guide to the Galaxy, in which the number 42 is The Answer to the Ultimate Question of Life, the Universe, and Everything. According to the fifth Hitchhiker volume, Mostly Harmless, 42 is the location of Stavromula Beta. Thus, 42 may be the world's longest written riddle, since the riddle of the question to the answer was raised in the first volume, and not answered until the final page of the fifth, and then passes unnoticed by the story's ever-bumbling characters. Douglas later (1994) created the 42 Puzzle, a game based on the number 42.
[edit] In other literature
Since Adams' book, people have looked for and found 42 in older literature, such as Shakespeare's plays and Carroll's Alice, which has 42 illustrations. In Chapter XII, the king explains "the oldest rule in the book": "Rule Forty-two. All persons more than a mile high [are] to leave the court". Carroll also uses the number in a line in The Hunting of the Snark : "He had forty-two boxes, all carefully packed..."
The first book to be printed with movable type, the Gutenberg Bible, is also known as the '42-line Bible', after the number of lines of print on each page.
In The Property of a Lady from Octopussy (the earlier editions of the three-part short story book included this story), James Bond (a character created by Ian Fleming) attended an auction to identify a top KGB spy. This spy was to raise the value of a Fabergé egg so that his female double agent working in MI5 (The British Secret Service) would get more money (as a way to monetarily pay her back for many years of service) from the sale of her (previously sent from Russia) Fabergé egg. The lot number of the Fabergé egg was 42.
In Rudyard Kipling's "The Travels of Captain Ryalls", 42 is the age at which Michael Ryalls first enters the jungle from his comfortable home in London. He travels with a 42 inch tall bull named Regis.
[edit] In music
- Level 42 is an English pop/rock band.
- "42" is one of the tracks on Coldplay's 2008 album Viva la Vida or Death and All His Friends.
- Strigaskór nr. 42 is an Icelandic band
- 42 is the title of a song by Philadelphia based jam/electronica band The Disco Biscuits
- "Forty-Two" is the title of a song from The Afters 'Never Going Back To OK' album, released February 26, 2008.
Arabic | ٤٢ |
Catalan | quaranta-dos |
Chinese | 四十二 |
Croatian | četrdeset i dva |
Czech | čtyřicet dva |
Danish | toogfyrre |
Dutch | tweeënveertig |
Esperanto | Kvardek Du |
Estonian | nelikümmend kaks |
French | quarante-deux |
German | zweiundvierzig |
Greek | σαράντα δύο |
Hebrew | מב (Mem Bet) |
Hungarian | negyvenkettő |
Italian | quarantadue |
Icelandic | fjörutíu og tveir |
Japanese | 四十二 (よんじゅうに) |
Korean | 사십이 (마흔둘) |
Latvian | četrdesmit divi |
Lietuvių | Keturiasdešimt du |
Lojban | vore |
Persian | چهل و دو |
Polish | czterdzieści dwa |
Portuguese | quarenta e dois |
Romanian | patruzeci şi doi |
Russian | сорок два |
Serbian | četiridesetdva |
Slovene | dvainštirideset |
Slovak | štyridsaťdva |
Spanish | cuarenta y dos |
Swedish | fyrtiotvå |
Turkish | kırk iki |
Suomeksi | neljäkymmentäkaksi |
Vietnamese | bốn mươi hai |
Welsh | pedwar-deg-dau, dau-ar-ddeugain |
[edit] In television and film
- The Kumars at No. 42 television series. In 2003, Sanjeev Bhaskar hosted a BBC show nominating The Hitchhiker's Guide to the Galaxy as Britain's Best Loved Book.
- 42 is one of The Numbers - 4, 8, 15, 16, 23, and 42 - featured in Lost.
- A made for TV movie 42: Forty Two Up - a documentary wherein the director revisits the same group of British-born adults after a 7 year wait.[8]
- 42 is an episode of Doctor Who, set in real time lasting approximately 42 minutes.
- In the television series and movie The X-Files, lead character Fox Mulder lives in apartment number 42
- In the television series Star Trek: The Next Generation the starship USS Enterprise (NCC-1701-D) has 42 decks.
- 42 is the name of Buzz Lightyear's space ship from Pixar's animated science fiction series Buzz Lightyear of Star Command.
- In an episode of "House M.D" Dr. House claims that his favorite number is 42.
- In A Clockwork Orange Alex browses through records in a record store and we see a record of the, at this time fictional, band Level 42.
- In Kiefer Sutherland's TV serial "24", the number 42 is reversed. Kiefer's birthdate is the 21st (of December), which is half of 42. Kiefer was born in 1966; 66 is 42 plus 24. Almost every season shows the number "42" at some point during one of the hours (as the minutes, i.e. "11:42").
[edit] In video games
- 42 Entertainment is the company responsible for several alternate reality games, including I Love Bees and Year Zero.
- In the PC game, Spore, reaching the center of the galaxy yields a powerful item known as the "Staff of Life" which has a limited 42 uses. It also grants the player an achievement titled "42".
- In the 2008 game Fable II, the last in a series of ancient artifacts the player can find says "Now just think of the number 42."
- 101010 (42 in Binary) is an open-source Java game.
[edit] In sports
- The jersey number of Jackie Robinson, which is the only number retired by all Major League Baseball teams. Although the number was retired in 1997, the last baseball players to wear number 42, Mariano Rivera of the New York Yankees, and Scott Vollmer, of the Akron Colts are currently still playing.
- The jersey number of football Hall of Famer, Ronnie Lott, safety for the San Francisco 49ers who retired his jersey number in 2003.
- The jersey number of Pat Tillman, which was retired on November 13, 2004 by Arizona State University.
- The number of laws of cricket.
- The number on Lee Petty's racing car in NASCAR. [9]
[edit] In technology
42 is a common magic number used by programmers:
- In the TIFF image file format, the second 16-bit word of every file is 42, which is used together with the first word to indicate byte order. In the reiser4 file system, 42 is the inode number of the root directory.
- In the ASCII character code and other codes based on it (ISO/IEC 8859-x, Unicode), 42 represents the asterisk character (*).
- The GNU C Library, a set of standard routines available for use in computer programming, contains a function—memfrob()—which performs an XOR combination of a given variable and the binary pattern 00101010 (42) as an XOR cipher.
- 42 is the result given by the web search engine Google when the query "the answer to life, the universe, and everything" is entered as a search (through Google's calculator).
[edit] In other fields
- Tower 42 is a skyscraper in the City of London, formerly known as the NatWest Tower.
- The name of a Texan trick-taking game played with dominoes (see 42 (dominoes)).
- In Japanese, 4 (shi) and 2 (ni) are together pronounced like "going to death" (死に). In Cantonese, 42 sounds like "easy death".
- In New York City, 42nd Street is a main and very popular two-way thoroughfare. Landmarks on it include the Chrysler Building, Grand Central Station, the main branch of the New York Public Library, and Times Square. The New York City street is also the setting for a movie by the same name (which also gave fame to its eponymous title song), and which later inspired a musical adaptation, 42nd Street.
- The UK government's controversial proposal to extend the time a suspect could be held without charge to 42 days was passed in the House of Commons with a majority of nine.
- Base 42 is a privately held web application company based in the Netherlands, 's-Hertogenbosch.
- 42 is the number of the French department Loire
- 10! (10 factorial) seconds is exactly 42 days.
[edit] Historical years
[edit] References
Wikimedia Commons has media related to: 42 (number) |
[edit] Footnotes
This article needs additional citations for verification. Please help improve this article by adding reliable references (ideally, using inline citations). Unsourced material may be challenged and removed. (October 2007) |
- ^ J. B. Conrey & A. Ghosh, "A conjecture for the sixth power moment of the Riemann zeta-function" International Mathematics Research Notices (1998)
- ^ J. B. Conrey & S. M. Gonek, "High moments of the Riemann zeta-function" Duke Math J. 107 3 (2001): 577 – 604
- ^ Alex Zhai ties for second-highest score in 2007 USA Mathematical Olympiad - By Andrew Lovdahl Gargoyle staff reporter Posted Monday, May 7, 2007, The OG, news & student awards - Online Gargoyle
- ^ CBC News staff, "Canadian math champ's skills add up to a perfect score" CBC News July 20, 2004. "A 16-year-old Canadian was one of four students who achieved a perfect score at an international mathematics competition. Jacob Tsimerman of Toronto scored 42 out of 42, making him one of 45 individual gold medallists at the 45th International Mathematical Olympiad in Athens."
- ^ "To Everywhere in 42 Minutes". http://www.time.com/time/magazine/article/0,9171,842469,00.html. Retrieved on 2008-05-18.
- ^ "Jumping into a 7,964 mile deep hole". http://www.youtube.com/watch?v=FAFUSbIs5KA. Retrieved on 2008-05-18.[dead link]
- ^ Primack, Joel; Nancy E. Abrams. "In A Beginning...Quantum Cosmology and Kabbalah" (PDF). http://physics.ucsc.edu/cosmo/primack_abrams/InABeginningTikkun1995.pdf. Retrieved on 2008-03-14.
- ^ http://www.imdb.com/title/tt0164312/ 42: Forty Two Up at IMDB
- ^ Allpar: Richard Petty and a history of Petty Racing