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56 (number)

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56 (number)

 ← 55 56 57 →
Cardinal fifty-six
Ordinal 56th
(fifty-sixth)
Factorization 23× 7
Divisors 1, 2, 4, 7, 8, 14, 28, 56
Roman numeral LVI
Binary 1110002
Ternary 20023
Quaternary 3204
Quinary 2115
Senary 1326
Octal 708
Duodecimal 4812
Vigesimal 2G20
Base 36 1K36

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

Contents

• Mathematics 1
• Science, technology, and biology 2
• Astronomy 3
• Music 4
• Television and film 5
• Sports 6
• Organizations 7
• People 8
• Geography 9
• Archaeology 10
• Cosmogony 11
• History 12
• Occultism 13
• References 14

Mathematics

56 is the sum of the first six triangular numbers (making it a tetrahedral number), as well as the sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17). It is also a tetranacci number and a pronic number. Adding up the divisors of 1 through 8 gives 56. Since 56 is twice a perfect number, it is itself a semiperfect number.

56 is a partition number - the number of distinct ways 11 can be represented as the sum of natural numbers.

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, 56 is an Erdős–Woods number.

The maximum determinant in an 8 by 8 matrix of zeroes and ones is 56.

Plutarch[1] 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 simple 'square and circle' geometry, a close approximation has recently been discovered which it is claimed[2] might have been used at Stonehenge.

56 is the only known number n such that 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 sum of the divisor function , see  A244439.

Organizations

• The symbol of the Hungarian Revolution of 1956.
• Famous Brazilian politician, Enéas Carneiro has an odd way of repeating the number of his party, "Fifty-Six" (cinquenta e seis, in Portuguese), making it a widely repeated jargon in his country.
• 56 Stuff, an international art community and a record label.
• Department 56 designer of collectibles, giftware and seasonal decorations such as miniature village houses.

People

• Shirley Temple, as a child, wore 56 curls in her hair. Curls were set by her mother who thus made sure of the exact number.
• Isoroku Yamamoto, named "Isoroku" because his father's age was 56 at his birth, and "Isoroku" is an old Japanese term meaning 56.

Cosmogony

• According to Aristotle, 56 is the number of layers of the Universe - Earth plus 55 crystalline spheres above it.[4]

Occultism

• There should be 56 cards in the Minor Arcana of a Tarot deck.

References

1. ^ V: 30MoraliaPlutarch,
2. ^ Pegs and Ropes: Geometry at Stonehenge
3. ^ Alexander, Caroline. "If the Stones Could Speak: Searching for the Meaning of Stonehenge". National Geographic Magazine. National Geographic Society. Retrieved 14 May 2013.
4. ^ Heaven by Lisa Miller, (2010), ISBN 978-0-06-055475-0 - page 13.
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