# six

six
6th
presentation
Roman VI
dual 110
Octal 6th
Duodecimal 6th
Morse code - · · · ·
Arabic ٦
Chinese
Mathematical properties
sign positive
parity straight
Factorization ${\ displaystyle 2 \ cdot 3}$
Divider 1, 2, 3, 6

The six (6) is the natural number between five and seven . She is straight .

## mathematics

Cube, cube or hexahedron

The 6 is the smallest composite number with two different prime factors, plus even the fourth highly composite number and the third triangular number .

It is the smallest perfect number : 6 = 1 + 2 + 3 and the factorial of 3 is , which is remarkable because there are no other three numbers whose product is equal to their sum . Likewise is . The equation has the only solution (without permutations ) x = 1, y = 2 and z = 3. Finally is${\ displaystyle 6 = 3! = 1 \ cdot 2 \ cdot 3}$${\ displaystyle 6 = {\ sqrt {1 ^ {3} + 2 ^ {3} + 3 ^ {3}}}}$${\ displaystyle x ^ {3} + y ^ {3} + z ^ {3} = 6xyz}$${\ displaystyle {\ frac {1} {1}} = {\ frac {1} {2}} + {\ frac {1} {3}} + {\ frac {1} {6}}}$

The cube , (from the Greek) hexahedron or (from the Latin) cube, is one of the five Platonic solids and has six equal faces. A tetrahedron has six edges and an octahedron has six corners. With regular hexagons you can fill a level completely .

The 6 is the two-dimensional kiss number ; H. You can put 6 (same size) coins / discs around another coin / disc of the same size so that all of them touch but no overlaps occur. It is also a Størmer number .

${\ displaystyle 6 = \ sum _ {n = 1} ^ {\ infty} {\ frac {n ^ {2}} {2 ^ {n}}} = {\ frac {1} {2}} + {\ frac {4} {4}} + {\ frac {9} {8}} + {\ frac {16} {16}} + \ cdots.}$

## Natural sciences

Hexipedes on a honeycomb
snowflakes

The insects , like all six-footed animals, have six legs.

Many crystals form hexagonal (hexagonal) structures, like natural ice , and snowflakes are six-pointed. In nature, the hexagonal shape can be found in the walls of the honeycomb , as there is an almost optimal ratio of wall material to room volume , hexagons cover the entire area .

## History and society

The 6 is at German schools , the least significant performance rating . At Swiss schools, grade 6 is the best grade.

In football, the number 6 on the back is the number of the defensive midfielder (also called the sixth position).

## Culture, literature, music and intellectual life

After the First World War, a group of neoclassical composers called Les Six (the six) gathered around the French writer Jean Cocteau .

6 takes! is a German card game.

## Mythology and religion

According to the Bible, God created the earth in six days (see Augustine 's remark in God's State ).

The Buddhism divides the world into six realms in which a being can be reborn. They are depicted on the Tibetan wheel of life .

The Star of David

The hexagram (six-pointed star), a star with six rays made up of two equilateral triangles placed on top of one another, is a religious symbol in some religions, such as Tantric Hinduism and Buddhism . As a Star of David ( Hebrew מגן דוד Magen David , 'Shield of David') is a symbol of Judaism and appears on the flag of Israel . Derived from this, it is a sign of alchemy , in which the overlapping triangles symbolize the elements. As the so-called brewer's star , the hexagram was the guild symbol of brewers and maltsters . The use in pub signs is derived from this.

The Book of Changes ( Yijing ) is based on sixty-four hexagrams , each made up of six Yin or Yang lines. For the meaning of the six in the Chinese number symbolism, see there.

## literature

• David Wells: The Penguin Dictionary of Curious and Interesting Numbers. corr. Edition. Penguin Books, London a. a. 1997, ISBN 0-14-026149-4 .