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6 (six) is the
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following 5 and preceding 7. It is a
composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
and the smallest
perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...
.


In mathematics

A six-sided
polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
is a
hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...
, one of the three
regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex ...
s capable of tiling the plane. A hexagon also has 6 edges as well as 6
internal and external angles In geometry, an angle of a polygon is formed by two adjacent edge (geometry), sides. For a simple polygon (non-self-intersecting), regardless of whether it is Polygon#Convexity and non-convexity, convex or non-convex, this angle is called an ...
. 6 is the second smallest
composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
. It is also the first number that is the sum of its proper divisors, making it the smallest
perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...
. It is also the only perfect number that doesn't have a
digital root The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit su ...
of 1. 6 is the first
unitary perfect number A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself. (A divisor ''d'' of a number ''n'' is a unitary divisor if ''d'' and ''n''/''d'' share no common factors). The numb ...
, since it is the sum of its positive proper
unitary divisor In mathematics, a natural number ''a'' is a unitary divisor (or Hall divisor) of a number ''b'' if ''a'' is a divisor of ''b'' and if ''a'' and \frac are coprime, having no common factor other than 1. Equivalently, a divisor ''a'' of ''b'' is a un ...
s, without including itself. Only five such numbers are known to exist. 6 is the largest of the four all-Harshad numbers. 6 is the 2nd
superior highly composite number In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to s ...
, the 2nd colossally abundant number, the 3rd triangular number, the 4th highly composite number, a pronic number, a congruent number, a harmonic divisor number, and a semiprime. 6 is also the first Granville number, or \mathcal-perfect number. A Golomb ruler of length 6 is a "perfect ruler". The six exponentials theorem guarantees that under certain conditions one of a set of six exponentials is Transcendental number, transcendental. The smallest non-abelian group is the symmetric group \mathrm which has factorial, 3! = 6 elements. 6 the answer to the two-dimensional kissing number problem. A cube has 6 Face (geometry), faces. A tetrahedron has 6 edges. In Four-dimensional space, four dimensions, there are a total of six Convex regular 4-polytope, convex regular polytopes. In the classification of finite simple groups, twenty of twenty-six sporadic groups in the Sporadic group#Organization, happy family are part of three families of groups which divide the order of the Monster group, friendly giant, the largest sporadic group: five ''first generation'' Mathieu groups, seven ''second generation'' subquotients of the Leech lattice, and eight ''third generation'' subgroups of the friendly giant. The remaining six sporadic groups do not divide the order of the friendly giant, which are termed the ''Pariah group, pariahs'' (Lyons group, ''Ly'', O'Nan group, ''O'N'', Rudvalis group, ''Ru'', Janko group J4, ''J''4, Janko group J3, ''J''3, and Janko group J1, ''J''1). 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


Greek and Latin word parts


'

' is classical Greek language#Periods, Greek for "six". Thus: *"Hexadecimal" combines ' with the Latinate ' to name a number base of 16 *A
hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...
is a
regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex ...
with six sides **' is a French nickname for the continental part of Metropolitan France for its resemblance to a hexagon#Regular hexagon, regular hexagon *A hexahedron is a polyhedron with six faces, with a cube (geometry), cube being a special case *Hexameter is a poetic form consisting of six feet per line *A "hex nut" is a nut (hardware), nut with six sides, and a hex Screw, bolt has a six-sided head *The prefix "" 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 (linguistics), 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. 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. 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 character for the digit 6 usually has an Ascender (typography), 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 snowflakes arises from the
hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...
al crystal structure of Ice, ordinary 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 numbers in Chinese culture, number in Chinese culture. *"Six" is used as an informal slang term for the British Secret Intelligence Service, MI6.


See also

*Six degrees (disambiguation).


References

* *''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


The Number 6The Positive Integer 6
{{DEFAULTSORT:6 (Number) Integers 6 (number)