# 6

(Redirected from )
 ← 5 6 7 →
Cardinal six
Ordinal 6th
(sixth)
Numeral system senary
Factorization 2 × 3
Divisors 1, 2, 3, 6
Roman numeral VI
Roman numeral (unicode) Ⅵ, ⅵ, ↅ
Greek prefix hexa-/hex-
Latin prefix sexa-/sex-
Binary 1102
Ternary 203
Quaternary 124
Quinary 115
Senary 106
Octal 68
Duodecimal 612
Vigesimal 620
Base 36 636
Greek στ (or ΣΤ or ς)
Arabic & Kurdish ٦
Persian ۶
Urdu
Amharic
Bengali
Chinese numeral 六，陆
Devanāgarī
Hebrew ו (Vav)
Khmer
Thai
Telugu
Tamil
Saraiki ٦

6 (six /ˈsɪks/) 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

A cube has 6 faces

Six is the smallest positive integer which is neither a square number nor a prime number.

Six is the second smallest composite number; its proper divisors are 1, 2 and 3.

Six is the smallest perfect number. Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.

Six is a triangular number, it is also an octahedral number.[1]

Six is the smallest natural number that can be written as the sum of two positive rational cubes which are not integers: ${\displaystyle 6=\left({\frac {17}{21}}\right)^{3}+\left({\frac {37}{21}}\right)^{3}.}$

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 six-sided polygon is called a hexagon. The hexagon is one of the three regular polygons capable of tiling the plane.

There are six basic trigonometric functions.

There are six convex regular polytopes in four dimensions.

The six exponentials theorem guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.

All primes above 3 are of the form 6n ± 1 for n ≥ 1.

### 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 25 50 100 1000
6 × x 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 150 300 600 6000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6 ÷ x 6 3 2 1.5 1.2 1 0.857142 0.75 0.6 0.6 0.54 0.5 0.461538 0.428571 0.4
x ÷ 6 0.16 0.3 0.5 0.6 0.83 1 1.16 1.3 1.5 1.6 1.83 2 2.16 2.3 2.5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
6x 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
x6 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809

## Greek and Latin word parts

### Hexa

Hexa is classical Greek for "six". Thus:

### The prefix sex-

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

• Senary is the ordinal adjective meaning "sixth"
• 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
• A group of six musicians is called a sextet
• Six babies delivered in one birth are sextuplets
• Sexy prime pairs - Prime pairs differing by six are sexy, because sex is the Latin word for six.[2]

## Evolution of the glyph

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 Brahmins of India, who wrote it in one stroke like a cursive lowercase e rotated 90 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.[3]

On the seven-segment displays of calculators and watches, 6 is usually written with six 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.

Just as in most modern typefaces, in typefaces with text figures the 6 character usually has an ascender, as, for example, in .

This numeral resembles an inverted 9. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.

## In music

A standard guitar has 6 strings

### In instruments

• A standard guitar has 6 strings
• Most woodwind instruments have 6 basic holes or keys (e.g., bassoon, clarinet, pennywhistle, saxophone); these holes or keys are usually not given numbers or letters in the fingering charts

### In music theory

• There are 6 whole tones in an octave.
• There are 6 semitones in a tritone.

### In works

• "Six geese a-laying" were given as a present on the sixth day in the popular Christmas carol, "The Twelve Days of Christmas."
• Divided in six arias, Hexachordum Apollinis is generally regarded as one of the pinnacles of Johann Pachelbel's oeuvre.
• The theme of the sixth album by Dream Theater, Six Degrees Of Inner Turbulence, was the number six: the album has six songs, and the sixth song — that is, the complete second disc — explores the stories of six individuals suffering from various mental illnesses.
• Aristotle gave six elements of tragedy, the first of which is Mythos.

## In science

### Chemistry

The cells of a beehive are 6-sided

### Medicine

• There are 6 tastes in traditional Indian Medicine called Ayurveda: sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body
• Phase 6 is one of six pandemic influenza phases

### Physics

In the Standard Model of particle physics, there are 6 types of quarks and 6 types of leptons
• In the Standard Model of particle physics, there are 6 types of quarks and 6 types of leptons
• In statistical mechanics, the six-vertex model has 6 possible configurations of arrows at each vertex
• There are six colors in the RGB color wheel: (primary) red, blue, green, (secondary) cyan, magenta, and yellow. (See Tertiary color)

## In sports

• The Original Six teams in the National Hockey League are Toronto, Chicago, Montreal, New York, Boston, and Detroit. They are the oldest remaining teams in the league, though not necessarily the first six; they comprised the entire league from 1942 to 1967
• Number of players:
• In association football (soccer), the number of substitutes combined by both teams, that are allowed in the game.
• In ice hockey, the number of players per team, including the goaltender, that are on the ice at any one time, excluding penalty situations.
• In volleyball, 6 players from each team on each side play against each other
• Six-man football is a variant of American or Canadian football, played by smaller schools with insufficient enrollment to field the traditional 11-man (American) or 12-man (Canadian) squad
• In most rugby league competitions (but not the European Super League, which uses static squad numbering), the jersey number 6 is worn by the starting five-eighth (Southern Hemisphere term) or stand-off half (Northern Hemisphere term).
• In rugby union, the starting blindside flanker wears jersey number 6. (Some teams use "left" and "right" flankers instead of "openside" and "blindside", with 6 being worn by the starting left flanker.)

## In the arts and entertainment

### Games

• The number of sides on a cube, hence the highest number on a standard die
• The six-sided tiles on a hex grid are used in many tabletop and board games.
• The highest number on one end of a standard domino

### Comics and cartoons

• The Super 6, an 1966 animated cartoon series featuring six different super-powered heroes.
• The Bionic Six are the heroes of the eponymous animated series
• Sinister Six is a group of super villains who appear in American comic books published by Marvel Comics

## References

1. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
2. ^ Chris K. Caldwell; G. L. Honaker Jr. (2009). Prime Curios!: The Dictionary of Prime Number Trivia. CreateSpace Independent Publishing Platform. p. 11. ISBN 978-1448651702.
3. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.66
4. ^ Mason, Robert (1983). Chickenhawk. London: Corgi Books. p. 141. ISBN 978-0-552-12419-5.
• 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
• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 67 - 69