6 (number)

From Academic Kids

<tr><td>Hebrew<td>ו (Vav)
Template:Numbers (digits)
Cardinal 6
six
Ordinal 6th
sixth
Numeral system senary
Factorization <math> 2 \cdot 3 <math>
Divisors 1, 2, 3, 6
Roman numeral VI
Unicode representation of Roman numeral Ⅵ, ⅵ
prefixes hexa-/hex- (from Greek)

sexa-/sex- (from Latin)

Binary 110
Octal 6
Duodecimal 6
Hexadecimal 6

6 (six) is the natural number following 5 and preceding 7.

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

Contents

Evolution of the glyph

Image:Evo6glyph.png

The evolution of our modern glyph for 6 appears rather simple when compared with that for the other numerals. Our modern 6 can be traced back to the Brahmin Indians, who wrote it in one stroke like a cursive lowercase e rotated 45 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 Ghubar 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.

In fonts with text figures, 6 usually has an ascender, for example, Missing image
TextFigs036.png
Image:TextFigs036.png

.

In mathematics

Six is the second smallest composite number, its proper divisors being 1, 2 and 3. Since six equals the sum of these proper divisors, six is a perfect number. As a perfect number, 6 is related to the Mersenne prime 3, since 21(22 - 1) = 6. The next perfect number is 28. Six is also a unitary perfect number, a harmonic divisor number and a highly composite number. The next highly composite number is 12.

The smallest non-abelian group is the symmetric group S3 which has 3! = 6 elements. S6 itself, with 720 elements, is the only finite symmetric group which has an outer automorphism.

In binary code, six is 110; in ternary code six is 20; in quaternary numeral system code six is 12; in quinary six is 11; in senary six is 10; in septenary code and all codes above (such as octal, decimal and hexadecimal) six is 6. Since it is divisible by the sum of its digits in all these bases, 6 is one of the four all-Harshad numbers.

A six-sided polygon is a hexagon. Figurate numbers representing hexagons (including six) are called hexagonal numbers. Six is also an octahedral number. It is a triangular number and so is its square (36).

In base 10, 6 is a 1-automorphic number.

In science

In astronomy,

Messier object M6, a magnitude 4.5 open cluster in the constellation Scorpius, also known as the Butterfly Cluster.
The New General Catalogue object (http://www.ngcic.org/) NGC 6, a spiral galaxy in the constellation Andromeda
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) of the solar eclipse series which began on -2691 March 16 and ended on -1393 May 3. The duration of Saros series 6 was 1298.1 years, and it contained 73 solar eclipses.
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) of the lunar eclipse series which began on -2642 July 25 and ended on -1091 February 10. The duration of Saros series 6 was 1550.6 years, and it contained 87 lunar eclipses.

In other fields

Six is:

  • In the ancient Roman calendar, Sextilis was the sixth month. After the Julian reform, June is the sixth month and Sextilis was renamed August.
  • Where Friday or Saturday is the sixth day of the week varies across cultures.
  • Sextidi was the sixth day of the decade in the French Revolutionary calendar.
  • In cricket, a "six" or "sixer" is a shot in which the ball clears the boundary without bouncing, scoring six runs. See cricket terminology.
  • In American Football, the number of points received for a touchdown.
  • In rugby union, the position of blindside flanker.
  • In baseball, six represents the shortstop's position.
  • In Australian Rules football, six points are received for a goal.
  • The length in years of a standard term of a United States senator.
  • The name of the smallest group of Cub Scouts, traditionally consisting of six people and is led by a 'sixer'. Logically speaking, this isn't always the case, particularly in packs with less than 6 Cub Scouts in it.
  • The number of cans in a six-pack.
  • The number of feet below ground level a coffin is traditionally buried; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead.
  • The number of inhabited continents, and the total number of continents if Eurasia (Europe plus Asia) is considered a single continent.
  • The number of large geyser fields in the world.
  • The number of points on a Star of David.
  • In Astrology, Virgo is the 6th astrological sign of the Zodiac.
  • The number of similar coins that can be arranged around a central seventh coin of the same kind so that each coin makes contact with the central one and touches both its neighbors without a gap; see also Sphere packing.
  • The number of strings on a standard guitar.
  • The number of basic holes or keys on most woodwind instruments (e.g., pennywhistle, clarinet, saxophone, bassoon). These holes or keys are usually not given numbers or letters in the fingering charts.
  • The first number where counting on your fingers requires two hands.
  • The number of sides on a cube, hence the highest number on a standard die.
  • The highest number on one end of a standard domino.

In addition:

Hexa is Greek for "six". Thus:

The prefix "hexa-" also occurs in the systematic name of many chemical compounds, such as "hexamethyl".

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

  • A group of six musicians is called a sextet.
  • Six babies delivered in one birth are sextuplets. The first set of sextuplets of whom all six survived are the Dilley Sextuplets.
  • 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.ca:Sis

da:6 (tal) de:Sechs es:Seis eo:Ses fr:6 (nombre) ko:6 ia:6 it:Sei he:6 (מספר) la:6 nah:Chicuace nl:Zes ja:6 no:6 (tall) nn:Talet 6 pl:Sześć sl:6 (število) sv:Sex th:6 (จำนวน) zh:6

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