6 ( six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.
In mathematics
A six-sided
polygon is a
hexagon,
one of the three
capable of
tessellation. A hexagon also has 6 edges as well as 6 internal and external angles.
6 is the second smallest composite number.
6 is the 2nd superior highly composite number,[Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 72]
The six exponentials theorem guarantees that under certain conditions one of a set of six exponentials is transcendental.
A cube has 6 faces. A tetrahedron has 6 edges. In four dimensions, there are a total of six convex regular polytopes.
In the classification of finite simple groups, twenty of twenty-six in the happy family are part of three families of groups which divide the order of the Monster group, the largest sporadic group: five first generation , seven second generation of the Leech lattice, and eight third generation of the friendly giant. The remaining six sporadic groups do not divide the order of the friendly giant, which are termed the Pariah group (Lyons group, O'N, Rudvalis group, J4, J3, and J1).
6 is the smallest integer which is not an exponent of a prime number, making it the smallest integer greater than 1 for which there does not exist a finite field of that size.
List of basic calculations
|
|
| 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 |
|
|
| 6 ÷ x | 6 | 3 | 2 | 1.5 | 1.2 | 1 | 0. | 0.75 | 0. | 0.6
! | 0. | 0.5 | 0. | 0. | 0.4 |
| x ÷ 6 | 0.1 | 0. | 0.5 | 0. | 0.8 | 1 | 1.1 | 1. | 1.5 | 1.
! | 1.8 | 2 | 2.1 | 2. | 2.5 |
|
|
| 6 | 6 | 36 | 216 | 1296 | 7776 | 46656 | 279936 | 1679616 | 10077696 | 60466176
! | 362797056 | 2176782336 | 13060694016 |
| x | 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:
-
"Hexadecimal" combines hexa- with the Latinate decimal to name a number base of 16
-
A hexagon is a regular polygon with six sides
-
L'Hexagone is a French nickname for the continental part of Metropolitan France for its resemblance to a regular hexagon
-
A hexahedron is a polyhedron with six faces, with a cube being a special case
-
Hexameter is a poetic form consisting of six feet per line
-
A "hex nut" is a nut with six sides, and a hex Screw has a six-sided head
-
The prefix "hexa-" also occurs in the systematic name of many chemical compounds, such as hexane which has 6 carbon atoms ().
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
-
Sexy prime pairs – Prime pairs differing by six are sexy, because sex is the Latin word for six.
The SI prefix for 10006 is exa- (E), and for its reciprocal atto- (a).
Evolution of the Hindu-Arabic digit
The evolution of the modern digit 6 appears to be more simple when compared with the other digits. The modern 6 can be traced back to the
Brahmi numerals of
India, which are first known from the Edicts of Ashoka .
It was written 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 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.
[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]
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 , in typefaces with text figures the character for the digit 6 usually has an ascender, as, for example, in .
This digit 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.
Chemistry
-
The sixfold symmetry of arises from the crystal structure of Ice.
Anthropology
-
A coffin is traditionally buried six feet under the ground; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead.
-
Six is a lucky number in Chinese culture.
["Chinese Numbers 1 to 10 | maayot". maayot • Bite-size daily Chinese stories. 2021-11-22. Retrieved 2025-01-17.]
-
"Six" is used as an informal slang term for the British Secret Intelligence Service, MI6.
Buddhism
Buddhism describes six realms of existence or realms into which beings can be reborn according to their deeds. They are visualised on the
Tibetan Buddhism wheel of life and illustrate the perpetual cyclical existence in
samsara. The six perfections or "
paramita" are among the best-known Buddhist symbols of the six. In
Mahayana Buddhism, these are fundamental spiritual qualities on the path of the
bodhisattva to achieve
nirvana.
See also
-
Six degrees (disambiguation).
-
A Property of the Number Six, Chapter 6, P Cameron, JH v. Lint, Designs, Graphs, Codes and their Links
-
Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 67 - 69
External links
