56 (number)

← 55 56 57 →
← 50 51 52 53 54 55 56 57 58 59 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fifty-six
Ordinal	56th (fifty-sixth)
Factorization	2^3× 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
Hexadecimal	3816
Vigesimal	2G20
Base 36	1K36

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

Mathematics

56 is:

• the sum of the first six triangular numbers (making it a tetrahedral number).^[1]
• the sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17).
• a tetranacci number^[2] and a pronic number.^[3]
• the sum of the sums of the divisors of the first 8 positive integers.^[4]
• 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.^[5]
• 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.

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

Plutarch^[6] 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^[7] might have been used at Stonehenge.

Science, technology, and biology

• The atomic number of barium.
• In humans, olfactory receptors are categorized in 56 families.
• The code for international direct dial phone calls to Chile.
• The maximum speed of analog data transmission over a POTS in the 20th century was 56 kbit/s.

Astronomy

• Messier object M56, a magnitude 9.5 globular cluster in the constellation Lyra.
• The New General Catalogue object NGC 56, an unverified object in the constellation Pisces. NGC 56 does not appear to be a real object.
• The Saros number of the solar eclipse series which began on -1172 July 17 and ended on 144 September. The duration of Saros series 56 was 1316.2 years, and it contained 74 solar eclipses.
• The Saros number of the lunar eclipse series which began on -852 May 7 and ended on 428 June. The duration of Saros series 56 was 1280.1 years, and it contained 72 lunar eclipses.

Music

• David Woodard's 2007 composition for piano, violin, cello and electronics, "56 Minutes".^[8][9]
• Christian punk rock band Flatfoot 56.
• "Along For The Ride ('56 T-bird)" sung by Danny O'Keefe.
  • This song was covered by John Denver.
• "Five Feet of Lovin '56" sung by Gene Vincent.
• Elvis Presley CD Elvis '56.
• The name of a Plexi song.
• Spanish Funk/Rock band Xperimento56.

Television and film

• The car number of Ray Peyton, Jr. (Breckin Meyer) in Herbie: Fully Loaded.
• "Nasser 56" documentary.
• Roberto, a character in Futurama, gets angered when Bender chooses the number "56-ish" when negotiating to spare his friends.

Sports

• In baseball, the number of consecutive games in which New York Yankees' Joe DiMaggio had a base hit in 1941, still a record.
• Hack Wilson hit 56 home runs in 1930, a National League record until the time of Mark McGwire.
• 56 people died in a fire at Valley Parade on May 11 in the Bradford City stadium fire

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.
• Avatar Meher Baba said there are always 56 God-realized human beings on the Earth at all times, at the head of the Spiritual Hierarchy.

Geography

• The name of the town Fifty-Six, Arkansas.
• The number of counties in the state of Montana.
• Cape Horn, the southernmost tip of South America, is located at almost exactly 56 degrees south.
• In the Los Angeles postal district, Zone 56 (now the ZIP Code area 90056) is one of few that is not within the Los Angeles City Limits (90020 and 90044 are others).
• 56 is the number of the French department Morbihan.
• China has 56 ethnic groups.
• There are 56 Longhurst codes.

Archaeology

• The number of Aubrey Holes (thought to have located wooden posts) in the first stage of Stonehenge.^[10]

Cosmogony

• According to Aristotle, 56 is the number of layers of the Universe - Earth plus 55 crystalline spheres above it.^[11]

History

• The number of men who signed the United States Declaration of Independence in 1776.
• The number of men of Netophah at the census of men of Israel upon return from exile (Ezra 2:22).

Occultism

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

References

1. "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. "Sloane's 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's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
6. Plutarch, Moralia V: 30
7. Pegs and Ropes: Geometry at Stonehenge
8. Currie, N., "Takemitsu and shakuhachi", Click Opera, Apr. 29, 2007.
9. Augustin Maurs bio, OVGuide.
10. Alexander, Caroline. "If the Stones Could Speak: Searching for the Meaning of Stonehenge". National Geographic Magazine. National Geographic Society. Retrieved 14 May 2013.
11. Heaven by Lisa Miller, (2010), ISBN 978-0-06-055475-0 - page 13.