6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.[1]

Quick Facts ← 5 6 7 →, Cardinal ...
5 6 7
−1 0 1 2 3 4 5 6 7 8 9
Cardinalsix
Ordinal6th
(sixth)
Numeral systemsenary
Factorization2 × 3
Divisors1, 2, 3, 6
Greek numeralϚ´
Roman numeralVI, vi, ↅ
Greek prefixhexa-/hex-
Latin prefixsexa-/sex-
Binary1102
Ternary203
Senary106
Octal68
Duodecimal612
Hexadecimal616
Greekστ (or ΣΤ or ς)
Arabic, Kurdish, Sindhi, Urdu٦
Persian۶
Amharic
Bengali
Chinese numeral六,陸
Devanāgarī
Gujarati
Hebrewו
Khmer
Thai
Telugu
Tamil
Saraiki٦
Malayalam
ArmenianԶ
Babylonian numeral𒐚
Egyptian hieroglyph𓏿
Morse code_ ....
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In mathematics

A six-sided polygon is a hexagon,[1] one of the three regular polygons capable of tiling the plane. A hexagon also has 6 edges as well as 6 internal and external angles.

6 is the second smallest composite number.[1] It is also the first number that is the sum of its proper divisors, making it the smallest perfect number.[2] 6 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.[3] 6 is the largest of the four all-Harshad numbers.[4]

6 is the 2nd superior highly composite number,[5] the 2nd colossally abundant number,[6] the 3rd triangular number,[7] the 4th highly composite number,[8] a pronic number,[9] a congruent number,[10] a harmonic divisor number,[11] and a semiprime.[12] 6 is also the first Granville number, or -perfect number. A Golomb ruler of length 6 is a "perfect ruler".[13]

The six exponentials theorem guarantees that under certain conditions one of a set of six exponentials is transcendental.[14] The smallest non-abelian group is the symmetric group which has 3! = 6 elements.[1] 6 the answer to the two-dimensional kissing number problem.[15]

A regular cube, with six faces

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 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).[16]

List of basic calculations

More information Multiplication ...
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
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More information Division ...
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
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More information Exponentiation ...
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
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Greek and Latin word parts

Hexa

Hexa is classical Greek for "six".[1] Thus:

  • "Hexadecimal" combines hexa- with the Latinate decimal to name a number base of 16[17]
  • A hexagon is a regular polygon with six sides[18]
  • A hexahedron is a polyhedron with six faces, with a cube being a special case[19]
  • Hexameter is a poetic form consisting of six feet per line
  • A "hex nut" is a nut with six sides, and a hex bolt 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 (C6H14).

The prefix sex-

Sex- is a Latin prefix meaning "six".[1] Thus:

  • Senary is the ordinal adjective meaning "sixth"[20]
  • 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.[21][22]

The SI prefix for 10006 is exa- (E), and for its reciprocal atto- (a).

Evolution of the Hindu-Arabic digit

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The first appearance of 6 is in the Edicts of Ashoka c.250 BCE. These are Brahmi numerals, ancestors of Hindu-Arabic numerals.
Thumb
The first known digit "6" in the number "256" in Ashoka's Minor Rock Edict No.1 in Sasaram, c.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 c.250 BCE.[23][24][25][26] 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.[27]

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 .[28]

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.

In music

Thumb
A standard guitar has six strings.

In artists

In instruments

  • A standard guitar has six strings[35]
  • 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

In music theory

  • There are six whole tones in an octave.[36]
  • There are six semitones in a tritone.[37]

In works

In religion

Judaism

Islam

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

Surah Qaf:38

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."

Others

In science

Astronomy

Biology

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The cells of a beehive are six-sided.

Chemistry

Thumb
A molecule of benzene has a ring of six carbon and six hydrogen atoms.

Medicine

  • 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.[61]
  • Phase 6 is one of six pandemic influenza phases.[62]

Physics

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In the Standard Model of particle physics, there are six types of quarks and six types of leptons.

In technology

6 as a resin identification code, used in recycling.
6 as a resin identification code, used in recycling.

In calendars

Anthropology

See also

References

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