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{{Infobox number
| number = 56
| divisor = 1, 2, 4, 7, 8, 14, 28, 56
}}
'''56''' ('''fifty-six''') is the [[natural number]] following [[55 (number)|55]] and preceding [[57 (number)|57]].


== Fifty-Six ==
== Mathematics ==
[[File:Regular polygon 56.svg|thumb|right|Regular 56-gon, associated by the Pythagoreans with [[Typhon]]]]
'''56''' is:


* The sum of the first six [[triangular number]]s (making it a [[tetrahedral number]]).<ref>{{Cite OEIS|1=A000292|2=Tetrahedral numbers|access-date=2016-05-30}}</ref>
[[Fifty-six_%28card_game%29|56 ]]is a more sophisticated variant of 28, also played in Kerala, using a double pack. This game is a trick taking game like 28. It is also similar to Norwegian JASS games. [[J9A10|J9A10]] is the World's First Online version of the [[Fifty-six_%28card_game%29| Card Game 56 ]].
* The number of ways to choose 3 out of 8 objects or 5 out of 8 objects, if order does not matter.
* The sum of six consecutive [[prime number|primes]] (3 + 5 + 7 + 11 + 13 + 17)
* a [[tetranacci number]]<ref>{{Cite OEIS|1=A000078|2=Tetranacci numbers|access-date=2016-05-30}}</ref> and as a multiple of 7 and 8, a [[pronic number]].<ref>{{Cite OEIS|1=A002378|2=Oblong (or promic, pronic, or heteromecic) numbers|access-date=2016-05-30}}</ref> Interestingly it is one of a few pronic numbers whose digits in decimal also are successive (5 and 6).
* a [[refactorable number]], since 8 is one of its 8 divisors.
* The sum of the sums of the divisors of the first 8 [[positive integers]].<ref>{{Cite OEIS|A024916|name=sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n}}</ref>
* A [[semiperfect number]], since 56 is twice a [[perfect number]].
* A [[partition number]] – the number of distinct ways 11 can be represented as the sum of natural numbers.
* An [[Erdős–Woods number]], since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member.<ref>{{Cite OEIS|1=A059756|2=Erdős-Woods numbers|access-date=2016-05-30}}</ref>
* The only known number n such that {{nowrap|φ(''n'' − 1)σ(''n'' − 1) {{=}} φ(''n'')σ(''n'') {{=}} φ(''n'' + 1)σ(''n'' + 1)}}, where φ(''m'') is [[Euler's totient function]] and σ(''n'') is the [[divisor function|sum of the divisor function]], see {{OEIS2C|id=A244439}}.
* The [[Hadamard's maximal determinant problem|maximum determinant]] in an 8 by 8 [[Matrix (mathematics)|matrix]] of zeroes and ones.
* The number of [https://oeis.org/A331452/a331452_12.png polygons formed by connecting all the 8 points on the perimeter of a two-times-two-square] by straight lines.<ref>{{Cite OEIS|1=A255011|access-date=2022-05-09}}</ref>


[[Plutarch]]<ref>[https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/B.html Plutarch, ''Moralia'' V: 30]</ref> states that the [[Pythagoreans]] associated a polygon of 56 sides with [[Typhon]] and that they associated certain polygons of smaller numbers of sides with other figures in Greek mythology. While it is impossible to construct a perfect regular 56-sided polygon using a compass and straightedge, a close approximation has recently been discovered which it is claimed<ref>[http://precedings.nature.com/documents/2153/version/1/html Pegs and Ropes: Geometry at Stonehenge]</ref> might have been used at Stonehenge, and it is constructible if the use of an [[angle trisector]] is allowed since 56 = 2<sup>3</sup> × 7.<ref name=Eekhoff>{{cite web|url=http://www.math.iastate.edu/thesisarchive/MSM/EekhoffMSMSS07.pdf |title=Constructibility of Regular Polygons |access-date=2015-02-19 |url-status=dead |archive-url=https://web.archive.org/web/20150714082609/http://www.math.iastate.edu/thesisarchive/MSM/EekhoffMSMSS07.pdf |archive-date=2015-07-14 }}</ref>
== J9A10 the first online version of 56 ==


== Organizations ==
[[J9A10]] is a group of a trick-taking games from [http://www.j9a10.com J9A10.com]. In these card games the Jack is the highest card in every suit, followed by the 9, Ace, 10, King and Queen. Of these cards only J, 9, A and 10 carry points or value and hence the name of the game.
* The symbol of the [[Hungarian Revolution of 1956]].
* [[Brazil]]ian politician, [[Enéas Carneiro]] has an odd way of repeating the number of his party, "Fifty-Six" ({{Lang|pt|cinquenta e seis}}, in [[Portuguese language|Portuguese]]), making it a widely repeated jargon in his country.


==Cosmogony==
These game have often been related to the European family of [[Jass]] games, played in the [[Netherlands]]. Variants of these games are played heavily in [[Kerala]], [[India]]. The most popular variant is the Card Game 56. Another variation of this 56 Card Game played in Kerala is the [[Twenty-eight_(card_game)| Card Game 28]].
* According to [[Aristotle]], 56 is the number of layers of the [[Universe]] – [[Earth]] plus 55 crystalline spheres above it.<ref>''Heaven'' by Lisa Miller, (2010), {{ISBN|978-0-06-055475-0}} - page 13.</ref>


==References==
[http://www.j9a10.com J9A10.com] has also committed to brining out more versions and variants of this game like the 28 Card Game and other similar variants of the [[J9A10]] [[Card Game]] family.
<references />


{{Integers|zero}}
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{{DEFAULTSORT:56 (Number)}}
[[Category:Integers]]

Latest revision as of 10:51, 6 January 2025

← 55 56 57 →
Cardinalfifty-six
Ordinal56th
(fifty-sixth)
Factorization23 × 7
Divisors1, 2, 4, 7, 8, 14, 28, 56
Greek numeralΝϚ´
Roman numeralLVI, lvi
Binary1110002
Ternary20023
Senary1326
Octal708
Duodecimal4812
Hexadecimal3816

56 (fifty-six) is the natural number following 55 and preceding 57.

Mathematics

[edit]
Regular 56-gon, associated by the Pythagoreans with Typhon

56 is:

Plutarch[7] states that the Pythagoreans associated a polygon of 56 sides with Typhon and that they associated certain polygons of smaller numbers of sides with other figures in Greek mythology. While it is impossible to construct a perfect regular 56-sided polygon using a compass and straightedge, a close approximation has recently been discovered which it is claimed[8] might have been used at Stonehenge, and it is constructible if the use of an angle trisector is allowed since 56 = 23 × 7.[9]

Organizations

[edit]

Cosmogony

[edit]

References

[edit]
  1. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  3. ^ 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.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A059756 (Erdős-Woods numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A255011". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-09.
  7. ^ Plutarch, Moralia V: 30
  8. ^ Pegs and Ropes: Geometry at Stonehenge
  9. ^ "Constructibility of Regular Polygons" (PDF). Archived from the original (PDF) on 2015-07-14. Retrieved 2015-02-19.
  10. ^ Heaven by Lisa Miller, (2010), ISBN 978-0-06-055475-0 - page 13.
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