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==Historical years==
==Historical years==
A.D. '''[[6]]''', [[6 BC|6 B.C.]], [[1906]], [[2006]], etc.
A.D. '''[[6]]''', [[6 BC|6 B.C.]], [[1906]], [[2006]], etc.
David Coulters number for WIshaw BC. Captain Dave 6.


== References ==
== References ==

Revision as of 01:20, 1 February 2007

Template:Numbers (digits)
Cardinal 6
six
Ordinal 6th
sixth
Numeral system senary
Factorization
Divisors 1, 2, 3, 6
Roman numeral VI
Roman numeral (Unicode) Ⅵ, ⅵ
prefixes hexa-/hex- (from Greek)

sexa-/sex- (from Latin)

Binary 110
Octal 6
Duodecimal 6
Hexadecimal 6
Hebrew ו (Vav)

6 (six) is the natural number following 5 and preceding 7.

The SI prefix for 10006 is exa (E), and for its reciprocal atto (a).

In mathematics

Six is the second smallest composite number, its proper divisors being 1, 2 and 3. Since six equals the sum of these proper divisors, six is a perfect number. As a perfect number, 6 is related to the Mersenne prime 3, since 21(22 - 1) = 6. The next perfect number is 28. Six is also a unitary perfect number, a harmonic divisor number and a highly composite number. The next highly composite number is 12.

5 and 6 form a Ruth-Aaron pair under either definition.

The smallest non-abelian group is the symmetric group S3 which has 3! = 6 elements.

S6, with 720 elements, is the only finite symmetric group which has an outer automorphism. This automorphism allows us to construct a number of exceptional mathematical objects such as the S(5,6,12) Steiner system, the projective plane of order 4 and the Hoffman-Singleton graph. A closely related result is the following theorem: 6 is the only natural number n for which there is a construction of n isomorphic objects on an n-set A, invariant under all permutations of A, but not naturally in 1-1 correspondence with the elements of A. This can also be expressed category theoretically: consider the category whose objects are the n element sets and whose arrows are the bijections between the sets. This category has a non-trivial functor to itself only for n=6.

Six similar coins can be arranged around a central coin of the same radius so that each coin makes contact with the central one (and touches both its neighbors without a gap), but seven cannot be so arranged. This makes 6 the answer to the two-dimensional kissing number problem. The densest sphere packing of the plane is obtained by extending this pattern to the hexagonal lattice in which each circle touches just six others.

6 is one of the four all-Harshad numbers.

A six-sided polygon is a hexagon, one of the three polygons capable of tiling the plane. Figurate numbers representing hexagons (including six) are called hexagonal numbers. Six is also an octahedral number. It is a triangular number and so is its square (36).

There are six basic trigonometric functions.

In numeral systems

Base Numeral system
2 binary 110
3 ternary 20
4 quaternary 12
5 quinary 11
6 senary 10
over 6 (decimal, hexadecimal)

In base 10, 6 is a 1-automorphic number.

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 300 600 6000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6 3 2 1.5 1.2 1 0.75 0.6 0.5 0.4
0.5 1 1.5 2 2.5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809

Evolution of the glyph

File:Evo6glyph.png

The evolution of our modern glyph for 6 appears rather simple when compared with that for the other numerals. Our modern 6 can be traced back to the Brahmin Indians, who wrote it in one stroke like a cursive lowercase e rotated 45 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Ghubar Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.

On the seven-segment displays of calculators and watches, 6 is usually written with six 6 segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on. For calculators that can display results in hexadecimal, a 6 that looks like a B is not practical.

In fonts with text figures, 6 usually has an ascender, for example, .

In science

  • The atomic number of carbon
  • The number of carbon atoms and carbon-carbon bonds in benzene
  • The number of known quarks
  • The number of tastes in traditional Indian Medicine called Ayurveda. They are: sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body

Astronomy

In religion

See also 666.

In music

In sports

  • In American and Canadian Football, the number of points received for a touchdown
  • In rugby union, the position of blindside flanker
  • In rugby league, the position of 5/8
  • In football/soccer, the number of Arsenal's legendary centre back and captain Tony Adams. The shirt was retired in 2002 on his retirement but has recently been passed on to Philippe Senderos.
  • In baseball, six represents the shortstop's position
  • In Australian Rules football, six points are received for a goal
  • In cricket, a "six" or "sixer" is a shot in which the ball clears the boundary without bouncing, scoring six runs. Also, there are six balls to an over in cricket. See cricket terminology
  • Retired number of former baseball players Stan Musial and Al Kaline
  • The number of goals Arsenal scored at Anfield to knock Liverpool out of the 2006-07 Carling Cup (only one more in numbers than the five times that Liverpool FC have won the European Cup, more than any other British club)
  • Before his retirement 6 was the number borne on the car of NASCAR driver Mark Martin.

In technology

File:6DN.jpg

In television

In other fields

International maritime signal flag for 6
  • The number 6 is often portrayed as an unlucky number
  • In the ancient Roman calendar, Sextilis was the sixth month. After the Julian reform, June became the sixth month and Sextilis was renamed August
  • Whether Thursday or Friday or Saturday is the sixth day of the week varies across cultures
  • Sextidi was the sixth day of the decade in the French Revolutionary calendar
  • The standard term in office for a United States senator is six years
  • Mark Martin's NASCAR racing number. 6 was also the number of David Pearson's car when he won his Nextel Cup Series Championship in 1966
  • The name of the smallest group of Cub Scouts, traditionally consisting of six people and is led by a 'sixer'. Logically speaking, this isn't always the case, particularly in packs with less than 6 Cub Scouts in it
  • The number of cans of soda or beer in a six-pack
  • The number of fundamental flight instruments lumped together on a cockpit display, called the six-pack.
  • The number of feet below ground level a coffin is traditionally buried; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead
  • The number of inhabited continents, and the total number of continents if Eurasia (Europe plus Asia) is considered a single continent
  • The number of large geyser fields in the world

Hexa is Greek for "six". Thus:

All insects have six legs.

The prefix "hexa-" also occurs in the systematic name of many chemical compounds, such as "hexamethyl"

Sex- is a Latin prefix meaning "six". Thus:

  • A group of six musicians is called a sextet
  • Six babies delivered in one birth are sextuplets. The first set of sextuplets of whom all six survived are the Dilley sextuplets
  • People with sexdactyly have six fingers on each hand
  • The measuring instrument called a sextant got its name because its shape forms one sixth of a whole circle
  • The ordinal adjective senary

Historical years

A.D. 6, 6 B.C., 1906, 2006, etc.

References

  • The Odd Number 6, JA Todd, Math. Proc. Camb. Phil. Soc. 41 (1945) 66--68
  • A Property of the Number Six, Chapter 6, P Cameron, JH v. Lint, Designs, Graphs, Codes and their Links ISBN 0-521-42385-6
  • Some Thoughts on the Number Six, John Baez