|
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. There are six convex regular polytopes in four dimensions. Six is the binary complement of number nine:
Six is also:
* In the ancient Roman calendar, Sextilis was the sixth month. After the Julian reform, June became the sixth month and Sextilis was renamed August
* 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
* In Astrology, Virgo is the 6th astrological sign of the Zodiac
* The number of sides on a cube, hence the highest number on a standard dice
* The highest number on one end of a standard domino
* The number of dots in a Braille cell.
* Les Six were a group of Lost Generation writers
* Extra-sensory perception is sometimes called the "sixth sense"
* Bands with the number six in their name include Eve 6, Slant 6, Sixpence None the Richer, Los Xey (sei is Basque for "six"), Vanity 6, and Electric Six
* Six Cardinal Directions: north, south, east, west, heaven, and land
* The Six Dynasties form part of Chinese history
* 6 is a lucky number in Chinese culture
* The Bionic Six are the heroes of an animated series
* The Birmingham Six were held in prison for 16 years
* Six Degrees of Kevin Bacon is a game that can be played with the names of actors and actresses
* 666 is considered the Number of the Beast
* There are 6 balls to an Over in Cricket
* In tarot, trump card No. 6 is "The Lovers".
* "Six" is used as an informal slang term for the British Secret Intelligence Service, MI6
* Six Flags amusement parks and theme parks
* the number of Australian states
|
|
