| ||||
---|---|---|---|---|
Cardinal | six | |||
Ordinal | 6th (sixth) | |||
Numeral system | senary | |||
Factorization | 2 × 3 | |||
Divisors | 1, 2, 3, 6 | |||
Greek numeral | Ϛ´ | |||
Roman numeral | VI, vi, ↅ | |||
Greek prefix | hexa-/hex- | |||
Latin prefix | sexa-/sex- | |||
Binary | 1102 | |||
Ternary | 203 | |||
Senary | 106 | |||
Octal | 68 | |||
Duodecimal | 612 | |||
Hexadecimal | 616 | |||
Greek | στ (or ΣΤ or ς) | |||
Arabic, Kurdish, Sindhi, Urdu | ٦ | |||
Persian | ۶ | |||
Amharic | ፮ | |||
Bengali | ৬ | |||
Chinese numeral | 六,陸 | |||
Devanāgarī | ६ | |||
Gujarati | ૬ | |||
Hebrew | ו | |||
Khmer | ៦ | |||
Thai | ๖ | |||
Telugu | ౬ | |||
Tamil | ௬ | |||
Saraiki | ٦ | |||
Malayalam | ൬ | |||
Armenian | Զ | |||
Babylonian numeral | 𒐚 | |||
Egyptian hieroglyph | 𓏿 | |||
Morse code | _ .... |
6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number. [1]
Six is the smallest positive integer which is neither a square number nor a prime number. It is the second smallest composite number after four, equal to the sum and the product of its three proper divisors (1, 2 and 3). [1] As such, 6 is the only number that is both the sum and product of three consecutive positive numbers. It is the smallest perfect number, which are numbers that are equal to their aliquot sum, or sum of their proper divisors. [1] [2] It is also the largest of the four all-Harshad numbers (1, 2, 4, and 6). [3]
6 is a pronic number and the only semiprime to be. [4] It is the first discrete biprime (2 × 3) [5] which makes it the first member of the (2 × q) discrete biprime family, where q is a higher prime. All primes above 3 are of the form 6n ± 1 for n ≥ 1.
As a perfect number:
Six is the first unitary perfect number , since it is the sum of its positive proper unitary divisors, without including itself. Only five such numbers are known to exist; sixty (10 × 6) and ninety (15 × 6) are the next two. [7]
It is the first primitive pseudoperfect number, [8] and all integers that are multiples of 6 are pseudoperfect (all multiples of a pseudoperfect number are pseudoperfect); six is also the smallest Granville number, or -perfect number. [9]
Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler". [10] Six is a congruent number. [11]
6 is the second primary pseudoperfect number, [12] and harmonic divisor number. [13] It is also the second superior highly composite number, [14] and the last to also be a primorial.
There are 6 non-equivalent ways in which 100 can be expressed as the sum of two prime numbers: (3 + 97), (11 + 89), (17 + 83), (29 + 71), (41 + 59) and (47 + 53). [15]
There is not a prime such that the multiplicative order of 2 modulo is 6, that is, By Zsigmondy's theorem, if is a natural number that is not 1 or 6, then there is a prime such that . See A112927 for such .
The ring of integer of the sixth cyclotomic field Q(ζ6), which is called Eisenstein integer, has 6 units: ±1, ±ω, ±ω2, where .
The six exponentials theorem guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials. [16]
There are six basic trigonometric functions: sin, cos, sec, csc, tan, and cot. [17]
The smallest non-abelian group is the symmetric group which has 3! = 6 elements. [1]
Six is a triangular number [18] and so is its square (36). It is the first octahedral number, preceding 19. [19]
A six-sided polygon is a hexagon, [1] one of the three regular polygons capable of tiling the plane. Figurate numbers representing hexagons (including six) are called hexagonal numbers. Because 6 is the product of a power of 2 (namely 21) with nothing but distinct Fermat primes (specifically 3), a regular hexagon is a constructible polygon with a compass and straightedge alone. A hexagram is a six-pointed geometric star figure (with the Schläfli symbol {6/2}, 2{3}, or {{3}}).
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. [20] 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.
There is only one non-trivial magic hexagon: it is of order-3 and made of nineteen cells, with a magic constant of 38. All rows and columns in a 6 × 6 magic square collectively generate a magic sum of 666 (which is doubly triangular). On the other hand, Graeco-Latin squares with order 6 do not exist; if is a natural number that is not 2 or 6, then there is a Graeco-Latin square of order . [21]
The cube is one of five Platonic solids, with a total of six squares as faces. It is the only regular polyhedron that can generate a uniform honeycomb on its own, which is also self-dual. The cuboctahedron, which is an Archimedean solid that is one of two quasiregular polyhedra, has eight triangles and six squares as faces. Inside, its vertex arrangement can be interpreted as three hexagons that intersect to form an equatorial hexagonal hemi-face, by-which the cuboctahedron is dissected into triangular cupolas. This solid is also the only polyhedron with radial equilateral symmetry, where its edges and long radii are of equal length; its one of only four polytopes with this property — the others are the hexagon, the tesseract (as the four-dimensional analogue of the cube), and the 24-cell. Only six polygons are faces of non-prismatic uniform polyhedra such as the Platonic solids or the Archimedean solids: the triangle, the square, the pentagon, the hexagon, the octagon, and the decagon. If self-dual images of the tetrahedron are considered distinct, then there are a total of six regular polyhedra that are formed by three different Weyl groups in the third dimension (based on tetrahedral, octahedral and icosahedral symmetries).
How closely the shape of an object resembles that of a perfect sphere is called its sphericity , calculated by: [22]
where is the surface area of the sphere, the volume of the object, and the surface area of the object.
In four dimensions, there are a total of six convex regular polytopes: the 5-cell, 8-cell, 16-cell, 24-cell, 120-cell, and 600-cell.
, with 720 = 6! 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, the four-dimensional 5-cell, and the Hoffman-Singleton graph. A closely related result is the following theorem: 6 is the only natural number for which there is a construction of isomorphic objects on an -set , invariant under all permutations of , but not naturally in one-to-one correspondence with the elements of . This can also be expressed category theoretically: consider the category whose objects are the element sets and whose arrows are the bijections between the sets. This category has a non-trivial functor to itself only for .
In the classification of finite simple groups, twenty of twenty-six sporadic groups in the happy family are part of three families of groups which divide the order of the 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 pariahs (Ly, O'N, Ru, J4, J3, and J1). [23]
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 |
Hexa is classical Greek for "six". [1] Thus:
Sex- is a Latin prefix meaning "six". [1] Thus:
The SI prefix for 10006 is exa- (E), and for its reciprocal atto- (a).
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 c. 250 BCE. [30] [31] [32] [33] 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. [34]
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 . [35]
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.
Indeed, We created the heavens and the earth and everything in between in six Days,1 and We were not ˹even˺ touched with fatigue.2
Note 1: The word day is not always used in the Quran to mean a 24-hour period. According to Surah Al-Hajj (The Pilgrimage):47, a heavenly Day is 1000 years of our time. The Day of Judgment will be 50,000 years of our time - Surah Al-Maarij (The Ascending Stairways):4. Hence, the six Days of creation refer to six eons of time, known only by Allah.
Note 2: Some Islamic scholars believe this verse comes in response to Exodus 31:17, which says, "The Lord made the heavens and the earth in six days, but on the seventh day He rested and was refreshed."
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
42 (forty-two) is the natural number that follows 41 and precedes 43.
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
45 (forty-five) is the natural number following 44 and preceding 46.
90 (ninety) is the natural number following 89 and preceding 91.
22 (twenty-two) is the natural number following 21 and preceding 23.
23 (twenty-three) is the natural number following 22 and preceding 24.
84 (eighty-four) is the natural number following 83 and preceding 85.
34 (thirty-four) is the natural number following 33 and preceding 35.
36 (thirty-six) is the natural number following 35 and preceding 37.
37 (thirty-seven) is the natural number following 36 and preceding 38.
360 is the natural number following 359 and preceding 361.
900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.
1729 is the natural number following 1728 and preceding 1730. It is notably the first nontrivial taxicab number.
257 is the natural number following 256 and preceding 258.
240 is the natural number following 239 and preceding 241.
353 is the natural number following 352 and preceding 354. It is a prime number.
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits.
40,000 is the natural number that comes after 39,999 and before 40,001. It is the square of 200.
slight ascenders that rise above the cap height ( in 4 and 6 )
The division of an octave into six equal parts is referred to as the whole-tone scale
Like the Tritone, it contains six semitones
Six geese a-laying
...the six arias with variations collected under the title Hexachordum Apollinis (1699)...
Six Degrees of Inner Turbulence
THE SIX QUALITATIVE ELEMENTS OF TRAGEDY
How the Six-pointed Star Became an Emblem for the Jewish People
Six orders of Mishnah
Six symbolic foods
it actually took only six days to create the earth
These works are recorded to have been completed in six days (the same day being six times repeated), because six is a perfect number
Shavuot falls on the sixth day of the Hebrew month of Sivan
...but seraphs, with six wings
Islam has six articles of faith
...it was blessed to fast for six days in the month of Shawwal...
...and the Six Ministries were made...
Three Messier objects are visible in this part of the sky : M6, M7 and M8 .
The cells of honeycombs are six-sided because a hexagon is the most material-efficient tessellation
Insects have six legs each...
...presently at least six kingdoms are recognized;
The acronym CHNOPS helps us remember these six elements
The benzene molecule has its six carbon atoms in a ring[ self-published source? ]
For example, the atomic number of carbon is 6,
snowflake, with its familiar sixfold rotational symmetry
Ayurvedic herbology is based on the tridoshic theory that there exist six basic tastes
The WHO Plan describes six phases of increasing public health risk associated with the emergence of a new influenza
...there are six types of quarks and six types of leptons.
Allowed configurations in the six-vertex model and their statistical weights
placing six primaries around the wheel in the following order: red, yellow, green, cyan, blue, magenta.
the Original Six
Indoor Lacrosse . This is played with six players per team
There are six players per team on the ice at one time.
In a regulation volleyball match with six players on each side of the court,
Augustus was also originally called Sextilis, the sixth month.
SEXTIDI, or " Jour de la Révolution, "
Roll two dice, a standard six-sided die numbered 1 through 6
Every Monday Blossom and Six ( who also...
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: CS1 maint: numeric names: authors list (link)Two of the luckiest numbers in China are '6' and '8'.
this is sometimes called a " sixth sense "