42 (number)

42 (forty-two) is the natural number that succeeds 41 and precedes 43.

Mathematics

Forty-two is a pronic number^[1] and an abundant number; its prime 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 is also a pronic number and 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. Additional properties of the number 42 include:

• It is the third primary pseudoperfect number.^[2]
• It is a Catalan number.^[3] 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 an alternating sign matrix number, that is, the number of 4-by-4 alternating sign matrices.
• It is the number of partitions of 10—the number of ways of expressing 10 as a sum of positive integers (note a different sense of partition from that above).

The 3 × 3 × 3 magic cube with rows summing to 42.

• 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, is composed of 3 numbers whose sum of values is 42.
• It is the third pentadecagonal number.^[4] It is a meandric number and an open meandric 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 that

  

  .

  where the infinite product is over all prime numbers, p.^[5][6]

• 42 is a Størmer number.^[7]
• 42 is the only known value that is the number of sets of four distinct positive integers a, b, c, d, each less than the value itself, such that ab − cd, ac − bd, and ad − bc are each multiples of the value. Whether there are other values remains an open question.^[8]
• 42 is a (2,6)-perfect number (super-multiperfect), as σ²(n) = σ(σ(n)) = 6n.^[9]
• 42 is the resulting number of the original Smith number (4937775 = 3 × 5 × 5 × 65837): Both the sum of its digits (4 + 9 + 3 + 7 + 7 + 7 + 5) and the sum of the digits in its prime factorization (3 + 5 + 5 + (6 + 5 + 8 + 3 + 7)) result in 42.
• The dimension of the Borel subalgebra in the exceptional Lie algebra e₆ is 42.
• 42 is the largest number n such that there exist positive integers p, q, r with 1 = 1/n + 1/p + 1/q + 1/r
• 42 is the smallest number k such that for every Riemann surface C, #Aut(C) ≤ k deg(K_C) = k(2g − 2) (Hurwitz's automorphisms theorem)
• In base 10, this number is a Harshad number^[10] and a self number,^[11] while it is a repdigit in base 4 (as 222).
• 42 is a perfect score on the USA Math Olympiad (USAMO)^[12] and International Mathematical Olympiad (IMO).^[13]
• 42 is the maximum of core points awarded in International Baccalaureate Diploma Programme.

Science

• 42 is the atomic number of molybdenum.
• 42 is the atomic mass of one of the naturally occurring stable isotopes of calcium.
• The angle rounded to whole degrees for which a rainbow appears (the critical angle).
• In 1966, 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, remove the air from the tube and fall through.^[14] 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. Even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity (known as a gravity train) always works out to be 42 minutes, so long as the tube remains friction-free, as while the force of gravity would be lessened, the distance traveled is reduced at an equal rate.^[15][16] (The same idea was proposed, without calculation by Lewis Carroll in 1893 in Sylvie and Bruno Concluded.^[17])

Technology

• Magic numbers used by programmers:
  • In TIFF (Tagged Image File Format), the second 16-bit word of every file is 42, "an arbitrary but carefully chosen number that further identifies the file as a TIFF file".
  • In the reiser4 file system, 42 is the inode number of the root directory.
  • In the military IRIG 106 Chapter 10 data recording standard, the hex value 0x464F52545974776F (ASCII "FORTYtwo") is used as a magic number to identify directory blocks.
• 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 engines Google and Wolfram Alpha when the query "the answer to life the universe and everything" is entered as a search.
• Tiling a plane using regular hexagons, which is honeycomb in appearance, is approximated in a topological sense to an accuracy of better than 1% using a stretcher bond brick pattern with bricks of 42 squares (6 by 7).^[18]
• The password expiration policy for a Microsoft Windows domain defaults to 42 days.^[19]

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 2004, asteroid 2001 DA₄₂ was given the permanent name 25924 Douglasadams, for the author Douglas Adams who popularized the number 42 and died in 2001. Brian G. Marsden, the director of the Minor Planet Center and the secretary for the naming committee, remarked that, with even his initials in the provisional designation, "This was sort of made for him, wasn't it?".
• Kepler-42, a red dwarf in the constellation Cygnus around which orbits the three smallest exoplanets found to date.
• 42 Isis, a large main-belt asteroid measuring about 100 km in diameter.

Religion

• In Japanese culture, the number 42 is considered unlucky because the numerals when pronounced separately—shi ni (four two)—sound like the word "death".^[20]
• There are 42 questions asked of persons making their journey through Death. Ma'at, a female personification, considered to be both maternal and a delivering force, is an Ancient Egyptian personification of physical and moral law, order, and truth. In the judgment scene described in the Egyptian and the Book of Pass (the Book of the Dead (which evolved from the Coffin Texts and the Pyramid Texts)), there are 42 questions personifying the analysis of Ma'at. If the departed reasonably can give answers to the 42 questions, they have the potential to either be reincarnate, or if completely successful, reach the ultimate goal of becoming a Star, whereon, they can continue to give Light, and fuel Universal growth.
• 42 is the number with which God creates the Universe in Kabbalistic 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").^[21] 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" "Emanation"). While there are obvious links between the Forty-Two Lettered Name of the Babylonian Talmud and the Kabbalah's Forty-Two Lettered Name, they are probably not identical because of the Kabbalah's emphasis on numbers. The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.
• 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 teenage boys who mocked Elisha for his baldness (2 Kings 2:23), etc.
• 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.
• The Gutenberg Bible is also known as the "42-line Bible", as the book contained 42 lines per page.
• The Forty-Two Articles (1552), largely the work of Thomas Cranmer, were intended to summarise Anglican doctrine, as it now existed under the reign of Edward VI.
• The Sutra of 42 Sections is a Buddhist scripture.

Popular culture

The Hitchhiker's Guide to the Galaxy

The Answer to the Ultimate Question of Life, The Universe, and Everything.

The number 42 is, in The Hitchhiker's Guide to the Galaxy by Douglas Adams, the "Answer to the Ultimate Question of Life, the Universe, and Everything", calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years. Unfortunately, no one knows what the question is. Thus, to calculate the Ultimate Question, a special computer the size of a small planet was built from organic components and named "Earth". The Ultimate Question "What do you get when you multiply six by nine"^[22] was found by Arthur Dent and Ford Prefect in the second book of the series, The Restaurant at the End of the Universe. This appeared first in the radio play and later in the novelization of The Hitchhiker's Guide to the Galaxy. The fact that Adams named the episodes of the radio play "fits", the same archaic title for a chapter or section used by Lewis Carroll in "The Hunting of the Snark", suggests that Adams was influenced by Carroll's fascination with and frequent use of the number. The fourth book in the series, the novel So Long, and Thanks for All the Fish, contains 42 chapters. According to the novel Mostly Harmless, 42 is the street address of Stavromula Beta. In 1994 Adams created the 42 Puzzle, a game based on the number 42.

The 2011 book 42: Douglas Adams' Amazingly Accurate Answer to Life, the Universe and Everything^[23] examines Adams' choice of the number 42 and also contains a compendium of some instances of the number in science, popular culture, and humour.

Works of Lewis Carroll

Lewis Carroll, who was a mathematician,^[24] made repeated use of this number in his writings.^[25]

Examples of Carroll's use of 42:

• Alice's Adventures in Wonderland has 42 illustrations.
• Alice's attempts at multiplication (chapter two of Alice in Wonderland) work if one uses base 18 to write the first answer, and increases the base by threes to 21, 24, etc. (the answers working up to 4 × 12 = "19" in base 39), but "breaks" precisely when one attempts the answer to 4 × 13 in base 42, leading Alice to declare "oh dear! I shall never get to twenty at that rate!"
• Rule Forty-two in Alice's Adventures in Wonderland ("All persons more than a mile high to leave the court").
• Rule 42 of the Code in the preface^[26] to The Hunting of the Snark ("No one shall speak to the Man at the Helm").
• In "fit the first" of The Hunting of the Snark the Baker had "forty-two boxes, all carefully packed, With his name painted clearly on each."^[26]
• The White Queen announces her age as "one hundred and one, five months and a day", which—if the best possible date is assumed for the action of Through the Looking-Glass—gives a total of 37,044 days. If the Red Queen, as part of the same chess set, is regarded as the same age, their combined age is 74,088 days, or 42 × 42 × 42.^[27]

Music

• Level 42 is an English pop/rock music band.
• "42" is one of the tracks on Coldplay's 2008 album Viva la Vida or Death and All His Friends.
• "Channel 42" is an electronic music song by deadmau5 featuring Wolfgang Gartner; it appears on the 2012 deadmau5 album Album Title Goes Here.

Television and film

• The Kumars at No. 42 television series
• "42" is an episode of Doctor Who, set in real time lasting approximately 42 minutes.
• On the game show Jeopardy!, "Watson" the IBM supercomputer, has 42 "threads" in its avatar.^[28]
• 42 Wallaby Way, Sydney, is the address for the dentist's office in Finding Nemo.^[29]
• 42 (film) is a film on the life of American baseball player Jackie Robinson.
• 42 is the number of Fox Mulder's apartment in the television series The X-Files.
• 42 is one of the six recurring numbers in the television series Lost.
• In the television series Supernatural the door to heaven is marked with the number 42.

Video games

• 42 Entertainment is the company responsible for several alternate reality games, including I Love Bees, Year Zero, and Why So Serious.
• Tokyo 42 is a videogame due for release in 2017.

• Squadron 42 is a videogame set in the Star Citizen Universe due for release in 2017.

Sports

Jackie Robinson in his now-retired number 42 jersey.

• 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, Mariano Rivera of the New York Yankees, the last professional baseball player to wear number 42, continued to wear it until he retired at the end of the 2013 season. As of the 2014 season, no player will ever again wear the number 42 in Major League Baseball except on Jackie Robinson Day (April 15), when all uniformed personnel (players, managers, coaches, and umpires) wear the number.
• The jersey number of basketball Hall of Famer and one of the 50 Greatest Players in NBA History James Worthy, small forward for the Los Angeles Lakers, who retired his jersey number in 1995.
• The jersey number of American football Hall of Fame, Ronnie Lott, safety for the San Francisco 49ers, who retired his jersey number in 2003.
• The jersey number of Chicago Bears legend Sid Luckman, which was retired by the Bears.
• The jersey number of American football player Pat Tillman, which was retired on November 13, 2004 by Arizona State University.
• The jersey number of baseball Hall of Famer Bruce Sutter, retired by the St. Louis Cardinals on September 17, 2006.
• The number of laws of cricket
• Rule 42 is the historic name of a Gaelic Athletic Association rule (now codified in Rule 5.1 and Rule 44) that in practice prohibits the playing of "foreign sports" (generally association football and the rugby codes) at GAA grounds.
• 42 is the number of a NASCAR car owned by Chip Ganassi Racing. As of 2016, it is driven by Kyle Larson.

Gaming

• The name of a Texan trick-taking game played with dominoes (see 42 (dominoes)).
• The number of spots (or pips, circular patches or pits) on a pair of standard six-sided dice.
• The board game Risk (game) has forty-two territories

Other fields

• +42 is the historic country calling code for the former country of Czechoslovakia.
• There are 42 US gallons in a barrel of oil.
• 42 is the number of the French department of Loire. The number is also reflected in the postal code for that area.
• Tower 42 is a skyscraper in the City of London, formerly known as the NatWest Tower.
• In New York City, 42nd Street is a main and very popular two-way thoroughfare. Landmarks on it include the Chrysler Building, Grand Central Terminal, the main branch of the New York Public Library, and Times Square. The Headquarters of the United Nations is at the east end of the street. 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.
• 42 is the inspiration for the name of the 42 Center of Excellence for Artificial Intelligence, based in Vienna, Austria^[30]
• 42 is the name of a private college of computer science and programming funded in Paris by the businessman and creator of Free, Xavier Niel.
• If one were to fold a piece of paper 42 times, it would reach beyond the orbit of the moon.^[31]
• 42 is the number of seats in Social Democratic Youth of Denmark's major council Hovedbestyrelsen. At the 2016 national convention, lowering the number of seats to 32 were discussed, but eventually the convention decided to stick with 42 members.

Other languages

References

External links

Look up forty-two in Wiktionary, the free dictionary.

• Grime, James; Gerardo Adesso; Phil Moriarty. "42 and Douglas Adams". Numberphile. Brady Haran. 
• My latest favorite Number: 42, John C. Baez
• The number Forty-two in real life

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