42 (number)

← 41 42 43 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-two
Ordinal	42nd (forty-second)
Factorization	2 × 3 × 7
Divisors	1, 2, 3, 6, 7, 14, 21, 42
Greek numeral	ΜΒ´
Roman numeral	XLII, xlii
Binary	1010102
Ternary	11203
Senary	1106
Octal	528
Duodecimal	3612
Hexadecimal	2A16

For other uses, see 42.

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

Mathematics

42 is a pronic number, ^[1] an abundant number ^[2] as well as a highly abundant number, ^[3] a practical number, ^[4] an admirable number, ^[5] and a Catalan number. ^[6]

The 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane. ^{[7] [8] [9] [a]}

42 is the only known ${\displaystyle k}$ that is equal to the number of sets of four distinct positive integers ${\displaystyle (a,b,c,d)}$ — each less than ${\displaystyle k}$ — such that ${\displaystyle {\text{ }}ab-cd,{\text{ }}}$${\displaystyle ac-bd{\text{ }}}$ and ${\displaystyle {\text{ }}ad-bc{\text{ }}}$ are all multiples of ${\displaystyle k}$. Whether there are other values remains an open question. ^[11]

42 is the magic constant of the smallest non-trivial magic cube, a ${\displaystyle 3\times 3\times 3}$ cube with entries of 1 through 27, where every row, column, corridor, and diagonal passing through the center sums to forty-two. ^{[12] [13]}

42 can be expressed as the sum of three cubes:$${\displaystyle 80,435,758,145,817,515^{3}+12,602,123,297,335,631^{3}+(-80,538,738,812,075,974)^{3}=42.}$$ ^[14]

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

Technology

• Magic numbers used by programmers:
  • In TIFF (Tag 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 ^[15] 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.
  • The password expiration policy for a Microsoft Windows domain defaults to 42 days. ^[16]

Wisdom Literature, Religion and Philosophy

• Abrahamic religions
  • In Judaism, by some traditions the Torah scroll is written with no fewer than 42 lines per column, based on the journeys of Israel. ^[17] In the present day, 42 lines is the most common standard, ^[18] 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"). ^[19] 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. ^[20]

Popular culture

The Hitchhiker's Guide to the Galaxy

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

Main article: Phrases from The Hitchhiker's Guide to the Galaxy §  The Answer to the Ultimate Question of Life, the Universe, and Everything is 42

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" ^[21] 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. ^[22]

Jackie Robinson

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 ever again wore 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.
  • 42 is a film on the life of American baseball player Jackie Robinson.
  • 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. ^[23]

Other

In Japanese culture, the number 42 is considered unlucky because the numerals when pronounced separately—shi ni (four two)—sound like the word "dying", ^[24] like the Latin word "mori".

Notes

1. Otherwise, 42 is also the difference between the number of diagonals and edges in a regular dodecagon, ^[10] which is the largest regular polygon that can tessellate space alongside other regular polygons (see, Euclidean tilings by convex regular polygons).

References

1. Sloane, N. J. A. (ed.). "SequenceA002378(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.). "SequenceA005101(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.). "SequenceA002093(Highly abundant numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-11-14.
4. Sloane, N. J. A. (ed.). "SequenceA005153(Practical numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-11-14.
5. Sloane, N. J. A. (ed.). "SequenceA111592(Admirable numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-11-14.
6. Sloane, N. J. A. (ed.). "SequenceA000108(Catalan numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
7. 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.
8. 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.
9. 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.
10. Sloane, N. J. A. (ed.). "SequenceA307681(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.
11. Kevin Brown. "Differently Perfect". MathPages.
12. 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.
13. Sloane, N. J. A. (ed.). "SequenceA027441(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.
14. 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.
15. 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.
16. "Maximum password age". Microsoft TechNet. Retrieved 15 January 2014.
17. 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.
18. 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.)
19. Joel Primack; Nancy E. Abrams. "In A Beginning...Quantum Cosmology and Kabbalah" (PDF). Retrieved 2008-03-14.
20. "The Prayer of the Kabbalist".
21. "Mathematical Fiction: Hitchhiker's Guide to the Galaxy (1979)" . Retrieved 30 November 2016. See this website for possible explanations of this seeming error.
22. "17 amazing Google Easter eggs". CBS News. November 11, 2011. Retrieved November 1, 2022.
23. 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.
24. Niiya, Brian. Japanese American history: an A-to-Z reference from 1868 to the present. Facts on File, Inc., 1993, p. 352

External links

Media related to 42 (number) at Wikimedia Commons

• Grime, James; Gerardo Adesso; Phil Moriarty. "42 and Douglas Adams". Numberphile. Brady Haran. Archived from the original on 2018-10-13. Retrieved 2013-04-08.
• My latest favorite Number: 42, John C. Baez
• The number Forty-two in real life