42 (number)

Last updated
41 42 43
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
Binary 1010102
Ternary 11203
Senary 1106
Octal 528
Duodecimal 3612
Hexadecimal 2A16

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

Contents

Mathematics

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] [lower-alpha 1]

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]

The 3 x 3 x 3 simple magic cube with rows summing to 42 Simple magic cube.svg
The 3 × 3 × 3 simple magic cube with rows summing to 42

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 is the number of (3, 3, 3) standard Young tableaux that use distinct entries [11] [12] (as well as the number of (2, 2, 2, 2, 2) tableaux). [13] [14]

42 can be expressed as the following sum of three cubes: [15]

Science

Technology

Astronomy

Wisdom Literature , Religion and Philosophy

The Hitchhiker's Guide to the Galaxy

The Answer to the Ultimate Question of Life, The Universe, and Everything Answer to Life.png
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" [37] 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. [38]

Works of Lewis Carroll

Lewis Carroll, who was a mathematician, [39] made repeated use of this number in his writings. [40]

Examples of Carroll's use of 42:

La Vita Nuova, Dante (1294)

Dante modeled the 42 chapters of his Vita Nuova on the 42 Stations of the Exodus. [45]

Music

Television and film

Video games

Sports

Jackie Robinson in his now-retired number 42 jersey Jrobinson.jpg
Jackie Robinson in his now-retired number 42 jersey

Architecture

Comics

Other fields

Other languages

Notes

  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).

Related Research Articles

10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

20 (twenty) is the natural number following 19 and preceding 21.

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

33 (thirty-three) is the natural number following 32 and preceding 34.

45 (forty-five) is the natural number following 44 and preceding 46.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or six dozen.

32 (thirty-two) is the natural number following 31 and preceding 33.

34 (thirty-four) is the natural number following 33 and preceding 35.

31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.

43 (forty-three) is the natural number following 42 and preceding 44.

48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

<span class="mw-page-title-main">360 (number)</span> Natural number

360 is the natural number following 359 and preceding 361.

126 is the natural number following 125 and preceding 127.

147 is the natural number following 146 and preceding 148.

135 is the natural number following 134 and preceding 136.

181 is the natural number following 180 and preceding 182.

168 is the natural number following 167 and preceding 169.

177 is the natural number following 176 and preceding 178.

14 (fourteen) is the natural number following 13 and preceding 15.

References

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  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.). "SequenceA000108(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.
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  10. 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.
  11. Sloane, N. J. A. (ed.). "SequenceA005789(3-dimensional Catalan numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-07.
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  32. 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.
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