Get 6 Number essential facts below. View Videos or join the 6 Number discussion. Add 6 Number to your PopFlock.com topic list for future reference or share this resource on social media.
Since 6 equals the sum of its proper divisors, it is a perfect number; 6 is the smallest of the perfect numbers.^{[1]} It is also the smallest Granville number, or ${\mathcal {S}}$-perfect number.^{[2]}^{[3]}
As a perfect number:
6 is related to the Mersenne prime 3, since . (The next perfect number is 28.)
6 is the only even perfect number that is not the sum of successive odd cubes.^{[4]}
6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one number; the square number, 25.
Six is the only number that is both the sum and the product of three consecutive positive numbers.^{[5]}
Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler".^{[6]} Six is a congruent number.^{[7]}
Six is the first discrete biprime (2 × 3) and the first member of the (2 × q) discrete biprime family.
There are no Graeco-Latin squares with order 6.^{[12]} If n is a natural number that is not 2 or 6, then there is a Graeco-Latin square with order n.
There is not a prime $p$ such that the multiplicative order of 2 modulo $p$ is 6, that is, $ord_{p}(2)=6$
By Zsigmondy's theorem, if $n$ is a natural number that is not 1 or 6, then there is a prime $p$ such that $ord_{p}(2)=n$. See A112927 for such $p$.
The ring of integer of the sixth cyclotomic field Q(?_{6}) , which is called Eisenstein integer, has 6 units: ±1, ±?, ±?^{2}, where $\omega ={\frac {1}{2}}(-1+i{\sqrt {3}})=e^{2\pi i/3}$.
S_{6}, 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 nisomorphic objects on an n-set A, invariant under all permutations of A, but not naturally in one-to-one 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 .
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.^{[13]} The densest sphere packing of the plane is obtained by extending this pattern to the hexagonallattice in which each circle touches just six others.
The six exponentials theorem guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.^{[18]}
All primes above 3 are of the form 6n ± 1 for n >= 1.
Sexy prime pairs - Prime pairs differing by six are sexy, because sex is the Latin word for six.^{[24]}^{[25]}
The SI prefix for 1000^{6} is exa- (E), and for its reciprocal atto- (a).
Evolution of the Arabic digit
The first appearance of 6 is in the Edicts of Ashoka circa 250 BCE. These are Brahmi numerals, ancestors of Hindu-Arabic numerals.
The first known digit "6" in the number "256" in Ashoka's Minor Rock Edict No.1 in Sasaram, circa 250 BCE
The evolution of our modern digit 6 appears rather 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 circa 250 BCE.^{[26]}^{[27]}^{[28]}^{[29]} 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.^{[30]}
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, as, for example, in .^{[31]}
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.
Most woodwind instruments have six 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
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.^{[43]}
Aristotle gave six elements of tragedy, the first of which is Mythos.^{[44]}
The six elements most common in biomolecules are called the CHNOPS elements; the letters stand for the chemical abbreviations of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur. See CHON.^{[59]}
Chemistry
A benzene molecule has a ring of six carbon atoms.^{[60]}
There are six tastes in traditional Indian medicine (Ayurveda): sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body.^{[63]}
The Original Six teams in the National Hockey League are Toronto, Chicago, Montreal, New York, Boston, and Detroit.^{[68]} 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 box lacrosse, the number of players per team, including the goaltender, that are on the floor at any one time, excluding penalty situations.^{[69]}
In ice hockey, the number of players per team, including the goaltender, that are on the ice at any one time during regulation play, excluding penalty situations. (Some leagues reduce the number of players on the ice during overtime.)^{[70]}
Six players from each team on each side play against each other.^{[71]}
Standard rules only allow six total substitutions per team per set. (Substitutions involving the libero, a defensive specialist who can only play in the back row, are not counted against this limit.)
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.^{[72]}
In Australian rules football, 6 points are awarded for a goal, scored when a kicked ball passes between the defending team's two inner goalposts without having been touched by another player.
In cricket, six runs are scored for the batting team when the ball is hit to the boundary or the ground beyond it without having touched the ground in the field.
In basketball, the ball used for women's full-court competitions is designated "size 6".^{[74]}
In most rugby league competitions (but not the Super League, which uses static squad numbering), the jersey number 6 is worn by the starting five-eighth (Southern Hemisphere term) or stand-off (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.)^{[75]}
In technology
On most phones, the 6 key is associated with the letters M, N, and O, but on the BlackBerry it is the key for J and K, and on the BlackBerry 8700 series and Curve 8900 with full keyboard, it is the key for F
Six is a modern retelling of the lives of the six wives of Henry VIII presented as a pop concert.^{[92]}
Anthropology
The name of the smallest group of Cub Scouts and Guiding's equivalent Brownies, traditionally consisting of six people and is led by a "sixer".
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^{[93]}
Six Flags is an American company running amusement parks and theme parks in the U.S., Canada, and Mexico.^{[103]}
In the U.S. Army "Six" as part of a radio call sign is used by the commanding officer of a unit, while subordinate platoon leaders usually go by "One".^{[104]} (For a similar example see also: Rainbow Six.)
^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
^"CHURCH FATHERS: City of God, Book XI (St. Augustine)". www.newadvent.org. Retrieved . These works are recorded to have been completed in six days (the same day being six times repeated), because six is a perfect number
^Bary, William Theodore De; DeBary, William T.; Chan, Wing-tsit; Lufrano, Richard; Ching, Julia; Johnson, David; Liu, Kwang-Ching; Mungello, David (1999). Sources of Chinese Tradition. Columbia University Press. ISBN978-0-231-11270-3. ...and the Six Ministries were made...
^Sedgwick, Marcus (2011-07-05). White Crow. Roaring Brook Press. p. 145. ISBN978-1-4299-7634-3. The cells of honeycombs are six-sided because a hexagon is the most material-efficient tessellation
^Sports, The National Alliance For Youth (2009-05-11). Coaching Volleyball For Dummies. John Wiley & Sons. p. 48. ISBN978-0-470-53398-7. In a regulation volleyball match with six players on each side of the court,
^Wilkinson, Endymion Porter; Wilkinson, Scholar and Diplomat (Eu Ambassador to China 1994-2001) Endymion (2000). Chinese History: A Manual. Harvard Univ Asia Center. p. 11. ISBN978-0-674-00249-4.