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42 (number)

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

← 41 42 43 →
Cardinalforty-two
Ordinal42nd
(forty-second)
Factorization2 × 3 × 7
Divisors1, 2, 3, 6, 7, 14, 21, 42
Greek numeralΜΒ´
Roman numeralXLII
Binary1010102
Ternary11203
Senary1106
Octal528
Duodecimal3612
Hexadecimal2A16

Mathematics

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42 is a pronic number[1] an abundant number,[2] and a Catalan number.[3]

Where the plane-vertex tiling 3.10.15 is constructible through elementary methods, the largest such tiling, 3.7.42, is not. This means that the 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane.[4][5][6][a]

42 is the only known   that is equal to the number of sets of four distinct positive integers   — each less than   — such that     and   are all multiples of  . Whether there are other values remains an open question.[8]

42 is the magic constant of the smallest non-trivial magic cube, a   cube with entries of 1 through 27, where every row, column, corridor, and diagonal passing through the center sums to forty-two.[9][10]

42 can be expressed as the following sum of three cubes: [11]

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

Science

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  • 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.[12] 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.[13][14] (The same idea was proposed, without calculation by Lewis Carroll in 1893 in Sylvie and Bruno Concluded.[15]) Now we know that is inaccurate, and it only would take about 38 minutes.[16]
  • As determined by the Babylonians, in 79 years, Mars orbits the Sun almost exactly 42 times.[17]
  • The hypothetical efficiency of converting mass to energy, as per   by having a given mass orbit a rotating black hole, is 42%, the highest efficiency yet known to modern physics.[18]
  • In Powers of Ten by Ray and Charles Eames, the known universe from large-scale to small-scale is represented by 42 different powers of ten. These powers range from 1025 meters to 10−17 meters.

Technology

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Astronomy

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Wisdom Literature, Religion and Philosophy

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  • Ancient Egyptian Wisdom Literature : Over most of pharaonic Egyptian history, the empire was divided into 42 nomes. Ancient Egyptian religion and mythological structure frequently model this terrestrial structure.[23]
    • 42 body parts of Osiris: In some traditions of the Osiris myth, Seth slays Osiris and distributes his 42 body parts all over Egypt. (In others, the number is fourteen and sixteen).[24]
    • 42 negative confessions: In Ancient Egyptian religion, the 42 negative confessions were a list of questions asked of deceased persons making their journey through the underworld after death. Ma'at was an abstract concept representing moral law, order, and truth in both the physical and moral spheres, as well as being an important goddess in the religion. In the judgment scene described in the Egyptian Book of the Dead, which evolved from the Coffin Texts and the Pyramid Texts, 42 questions were asked of the deceased person as part of the assessment of Ma'at. If the deceased person could reasonably give answers to the 42 questions, they would be permitted to enter the afterlife. These 42 questions are known as the "42 Negative Confessions" and can be found in funerary texts such as the Papyrus of Ani.
    • 42 books in the core library: Clement of Alexandria states that the Egyptian temple library is divided into 42 "absolutely necessary" books that formed the stock of a core library. 36 contain the entire philosophy of the Egyptians which are memorized by the priests. While the remaining 6, are learned by the Pastophoroi (image-bearers).[25][26] (36 is like-wise a sacred number in Egyptian thought, related to time, in particular the thirty-six Decan stars and the thirty-six, 10-day "weeks" in the Egyptian year.[27]) The 42 books were not canonized like the Hebrew bible; they only supported and never replaced temple ritual. Hence, the destruction of the Egyptian temples and the cessation of the rituals ended Egyptian cultural continuity.[28]
  • Abrahamic religions
    • In Ezra 2:24, 42 men of Beth-azmaveth were counted in the census of men of Israel upon return from exile; 2 Kings 2:24, God, because of a "curse" Elisha put on them, sent/allowed bears to maul 42 teenage boys who mocked Elisha for his baldness.
    • In Judaism, by some traditions the Torah scroll is written with no fewer than 42 lines per column, based on the journeys of Israel.[29] In the present day, 42 lines is the most common standard,[30] but various traditions remain in use (see Sefer Torah).
    • 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").[31] 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. 42 letters make the Ana beKo'ach prayer.[32]
    • 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.
    • Hebrew Bible & Book of Revelation: “For a thousand years in your sight are like a day that has just gone by, or like a watch in the night.” (Psalm 90:4)→ “Fear God and give Him glory, because the hour of His judgment has come. Worship the One who made the heavens and the earth and the sea and the springs of waters.” (Revelation 14:7)→ 1,000 years per day/24 hours per day ≈ 42 years/hour; it is prophesied that for 42 months the Beast will hold dominion over the Earth (Revelation 13:5); etc.
    • 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 summarize Anglican doctrine, as it now existed under the reign of Edward VI.
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The Hitchhiker's Guide to the Galaxy

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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"[34] is 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 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. Adams says he picked the number simply as a joke, with no deeper meaning.

Google also has a calculator easter egg when one searches "the answer to the ultimate question of life, the universe, and everything." Once typed (all in lowercase), the calculator answers with the number 42.[35]

Works of Lewis Carroll

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Lewis Carroll, who was a mathematician,[36] made repeated use of this number in his writings.[37]

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!"[38]
  • 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[39] 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."[40]
  • 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 (e.g., a date is chosen such that the rollover from February to March is excluded from what would otherwise be an imprecise measurement of "five months and a day")—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.[41]

La Vita Nuova, Dante (1294)

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Dante modeled the 42 chapters of his Vita Nuova on the 42 Stations of the Exodus.[42]

Music

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Television and film

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  • The Kumars at No. 42 is a British comedy 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.[44]
  • 42 is a film on the life of American baseball player Jackie Robinson.
  • Captain Harlock is sometimes seen wearing clothing with the number 42 on it.
  • In the Stargate Atlantis season 4 episode "Quarantine", Colonel Sheppard states that Dr. McKay's password ends in 42 because "It's the ultimate answer to the great question of life, the universe and everything."
  • In Star Wars: The Rise of Skywalker, the Festival of the Ancestors on Planet Pasaana is held every 42 years. The film itself was released in 2019, 42 years after the 1977 original Star Wars film. By a "whole string of pretty meaningless coincidences",[45] 2019 is the same year that 42 was found to be the largest possible natural number less than 100 to be expressed as a sum of three cubes.[11]
  • In the TV show Lost, 42 is one of the numbers used throughout the show for some of its mysteries.
  • There is a Belgian TV drama called Unit 42 about a special police unit that uses high-tech tools to go after criminals. One of the characters in the pilot episode explains that the unit was named based on the Hitchhiker's Guide To The Galaxy.

Video games

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Sports

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Jackie Robinson in his now-retired number 42 jersey

Architecture

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  • The architects of the Rockefeller Center in New York City worked daily in the Graybar Building where on "the twenty-fifth floor, one enormous drafting room contained forty-two identical drawing boards, each the size of a six-seat dining room table; another room harboured twelve more, and an additional fourteen stood just outside the principals' offices at the top of the circular iron staircase connecting 25 to 26".[47]
  • In the Rockefeller Center (New York City) there are a total of "forty-two elevators in five separate banks"[48] which carry tenants and visitors to the sixty-six floors.

Comics

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  • Miles Morales was bitten by a spider bearing the number 42, causing him to become a Spider-Man. The number was later heavily referenced in the film Spider-Man: Into the Spider-Verse. The use of 42 within the franchise references Jackie Robinson's use of the number, though many fans incorrectly believed it to be a Hitchhiker's Guide to the Galaxy reference.[49]

Other fields

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Other languages

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Notes

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  1. ^ Otherwise, 42 is also the difference between the number of diagonals and edges in a regular dodecagon,[7] which is the largest regular polygon that can tessellate space alongside other regular polygons (see, Euclidean tilings by convex regular polygons).

References

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  1. ^ Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ 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 2024-01-07.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  4. ^ Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. 50 (5). Taylor & Francis, Ltd.: 229–230. doi:10.2307/2689529. ISSN 0025-570X. JSTOR 2689529. S2CID 123776612. Zbl 0385.51006.
  5. ^ Dallas, Elmslie William (1855). "Part II. (VII): Of the Circle, with its Inscribed and Circumscribed Figures − Equal Division and the Construction of Polygons". The Elements of Plane Practical Geometry. London: John W. Parker & Son, West Strand. p. 134.
  6. ^ Jardine, Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A307681 (Difference between the number of diagonals and the number of sides for a convex n-gon.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-25.
  8. ^ Kevin Brown. "Differently Perfect". MathPages.
  9. ^ Andrews, William Symes (1960). Magic Squares and Cubes (PDF) (2nd ed.). New York: Dover Publications. p. 65. doi:10.2307/3603128. ISBN 9780486206585. JSTOR 3603128. MR 0114763. OCLC 1136401. S2CID 121770908. Zbl 1003.05500.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A027441 (a(n) equal to (n^4 + n)/2 (Row sums of an n X n X n magic cube, when it exists).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
  11. ^ a b Booker, Andrew R.; Sutherland, Andrew V. (2021). "On a question of Mordell". Proceedings of the National Academy of Sciences. 118 (11). arXiv:2007.01209. Bibcode:2021PNAS..11822377B. doi:10.1073/pnas.2022377118. PMC 7980389. PMID 33692126.
  12. ^ Cooper, Paul W. (1966). "Through the Earth in Forty Minutes". American Journal of Physics. 34 (1): 68–69. Bibcode:1966AmJPh..34...68C. doi:10.1119/1.1972773.
  13. ^ "To Everywhere in 42 Minutes". Time. February 11, 1966. Archived from the original on 12 May 2008. Retrieved 2008-05-18.
  14. ^ "Jumping into a 7,965 mile deep hole". YouTube. Archived from the original on June 2, 2008. Retrieved 2008-05-18.
  15. ^ Carroll, Lewis (29 December 1893). "Chapter 7". Sylvie and Bruno Concluded. Vol. 2. illustrated by Harry Furniss. United Kingdom: Macmillan and Co. Each railway is in a long tunnel, perfectly straight: so of course the middle of it is nearer the centre of the globe than the two ends: so every train runs half-way down-hill, and that gives it force enough to run the other half up-hill.
  16. ^ Choi, Charles Q. (March 31, 2015). "How Long Would It Take to Fall Through the Earth?". livescience.com. Retrieved 2021-06-27.
  17. ^ Powell, Martin J. "Ancient astronomy and the naked-eye planets". Eternal Gadgetry. MS. Retrieved January 6, 2018.
  18. ^ Cotter, Garrett (2012). "High-Energy Astrophysics Lecture" (PDF). Astrophysics | University of Oxford Department of Physics.
  19. ^ Berard (April 2009). "IRIG 106 Telemetry Standard Chapter 10" (PDF). U.S. Army White Sands Missile Range, New Mexico: Range Commanders Council. Archived (PDF) from the original on 2020-11-12. Retrieved 2010-11-10.
  20. ^ Lee Middleton; Jayanthi Sivaswamy (2002). "Framework for practical hexagonal-image processing". Journal of Electronic Imaging. 11 (104): 104. Bibcode:2002JEI....11..104M. doi:10.1117/1.1426078.
  21. ^ "Maximum password age". Microsoft TechNet. Retrieved 15 January 2014.
  22. ^ "Ethereum Blocks #0". Etherscan.
  23. ^ Assman, Jan (2008). Of God and Gods: Egypt, Israel, and the Rise of Monotheism (George L. Mosse Series in Modern European Cultural and Intellectual History) (Kindle ed.). The University of Wisconsin Press. p. Kindle Location 195. ISBN 978-0299225544.
  24. ^ Assman, Jan (2008). Of God and Gods: Egypt, Israel, and the Rise of Monotheism (George L. Mosse Series in Modern European Cultural and Intellectual History) (Kindle ed.). The University of Wisconsin Press. p. Kindle Location 576. ISBN 978-0299225544.
  25. ^ Assman, Jan (2008). Of God and Gods: Egypt, Israel, and the Rise of Monotheism (George L. Mosse Series in Modern European Cultural and Intellectual History) (Kindle ed.). The University of Wisconsin Press. p. Kindle Location 1364. ISBN 978-0299225544.
  26. ^ Clement of Alexandria (1885). "Book VI:IV". In Roberts, Alexander; James, Sir; Coxe, Arthur (eds.). The Stromata, or Miscellanies (With Active Table of Contents) (Kindle ed.). p. Kindle Location 11498.
  27. ^ Assman, Jan (2008). Of God and Gods: Egypt, Israel, and the Rise of Monotheism (George L. Mosse Series in Modern European Cultural and Intellectual History) (Kindle ed.). The University of Wisconsin Press. p. Kindle Location 1380. ISBN 978-0299225544.
  28. ^ Assman, Jan (2008). Of God and Gods: Egypt, Israel, and the Rise of Monotheism (George L. Mosse Series in Modern European Cultural and Intellectual History) (Kindle ed.). The University of Wisconsin Press. p. Kindle Location 1418. ISBN 978-0299225544.
  29. ^ Ganzfried, R. Solomon (1902). קסת הסופר [Keset haSofer] (in Hebrew and English). Translated by Friendman, Jen (First ed.). Bardejov: דפוס יוסף מאיר בלייער. It is the custom to have no fewer than 48 lines, representing the journeys of Israel, and some say no fewer than 42, because of what God did in the Sinai wilderness at Kadesh. Also, we don't have more than 60 lines, representing the 60 myriads of Israel who received the Torah.
  30. ^ Jacobs, Joseph; Eisenstein, Judah; Executive Committee of the Editorial Board; Blau, Ludwig (1906). "Scroll of the Law (Hebrew, "Sefer Torah")". Jewish Encyclopedia. Retrieved 12 February 2020. (At the present day the forty-two-lined column is the generally accepted style of the scroll, its length being about 24 inches.)
  31. ^ Joel Primack; Nancy E. Abrams. "In A Beginning...Quantum Cosmology and Kabbalah" (PDF). Retrieved 2008-03-14.
  32. ^ "The Prayer of the Kabbalist".
  33. ^ Niiya, Brian. Japanese American history: an A-to-Z reference from 1868 to the present. Facts on File, Inc., 1993, p. 352
  34. ^ "Mathematical Fiction: Hitchhiker's Guide to the Galaxy (1979)". Retrieved 30 November 2016. See this website for possible explanations of this seeming error.
  35. ^ "17 amazing Google Easter eggs". CBS News. November 11, 2011. Retrieved November 1, 2022.
  36. ^ "Lewis Carroll and Douglas Adams – Word Ways – Find Articles". 29 June 2012. Archived from the original on 29 June 2012.
  37. ^ The Mystery of Lewis Carroll, Jenny Woolf
  38. ^ Watkins, John J. (2009). "Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life: An Agony in Eight Fits by Robin Wilson: New York, NY, London, W. W. Norton & Company, Inc., 2008, xii + 237 pp., US $24.95, ISBN 978-0-393-06027-0". The Mathematical Intelligencer. 31 (4): 60–62. doi:10.1007/s00283-009-9070-x. ISSN 0343-6993.
  39. ^ Carroll, Lewis. "The Hunting of the Snark".
  40. ^ Carroll, Lewis. "The Hunting of the Snark".
  41. ^ What Lewis Carroll Taught Us: Alice's creator knew all about role-playing. by Seth Lerer, March 4, 2010
  42. ^ Julia Bolton Holloway, Sweet New Style: Brunetto Latino, Dante Alighieri and Geoffrey Chaucer, Chapter III, (2003)
  43. ^ Walker, Carter (2016-07-15). "REVIEW: Music, not problems, is focus this year at Disco Biscuits' Camp Bisco at Pavilion at Montage". baltimoresun.com. Retrieved 2020-08-17.
  44. ^ "Watson Jeopardy! computer: Ken Jennings describes what it's like to play against a machine". Slate. Retrieved 2 October 2015.
  45. ^ Adams, Douglas (September 29, 2010). The Ultimate Hitchhiker's Guide to the Galaxy (Kindle ed.). Del Ray. p. 27. ISBN 978-0-307-49846-5.
  46. ^ "The Laws of Cricket". Archived from the original on 29 August 2017. Retrieved 26 January 2017.
  47. ^ Okrent, Daniel. Great Fortune: the Epic of the Rockefeller Centre. Viking Penguin, 2003, p. 147
  48. ^ Okrent, Daniel. Great Fortune: the Epic of the Rockefeller Centre. Viking Penguin, 2003, p. 162
  49. ^ Renfro, Kim (February 26, 2019). "Why the number 42 was hidden in plain sight throughout 'Spider-Man: Into the Spider-Verse'". Insider Inc. Retrieved November 29, 2019.
  50. ^ "Tower 42 – City of London". cityoflondon.gov.uk. Retrieved 23 October 2018.
  51. ^ "42: Neues KI-Start-up von Jajah-Gründer Daniel Mattes". Futurezone. 22 November 2015. Retrieved 2015-11-22.
  52. ^ BigThink.com How many times must you fold a paper to reach the Moon?, January 8, 2024
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