subject: Article 8 [print this page] 8 (eight) is the natural number following 7 and preceding 9. The SI prefix for 10008 is yotta (Y), and for its reciprocal yocto (y). It is the root of two other numbers: eighteen (eight and ten) and eighty (eight tens). Linguistically, it is derived from Middle English eighte 8 is a composite number, its proper divisors being 1, 2, and 4. It is twice 4 or four times 2. Eight is a power of two, being 23 (two cubed), and is the first number of the form p3. It has an aliquot sum of 7 in the 4 member aliquot sequence (8,7,1,0) being the first member of 7-aliquot tree. It is symbolized by the Arabic numeral (figure) 8. All powers of 2 ;(2x), have an aliquot sum of one less than themselves. Eight is the first number to be the aliquot sum of two numbers other than itself; the discrete biprime 10, and the square number 49. 8 is the base of the octal number system, which is mostly used with computers. In octal, one digit represents 3 bits. In modern computers, a byte is a grouping of eight bits, also called an octet. The number 8 is a Fibonacci number, being 3 plus 5. The next Fibonacci number is 13. 8 is the only Fibonacci number that is a perfect cube.[1] 8 and 9 form a RuthAaron pair under the second definition in which repeated prime factors are counted as often as they occur. A polygon with eight sides is an octagon. Figurate numbers representing octagons (including eight) are called octagonal numbers. A polyhedron with eight faces is an octahedron. A cuboctahedron has as faces six equal squares and eight equal regular triangles. A cube has eight verticies. Sphenic numbers always have exactly eight divisors. 8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra. The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity We also see a period of 8 in the K-theory of spheres and in the representation theory of the rotation groups, the latter giving rise to the 8 by 8 spinorial chessboard. All of these properties are closely related to the properties of the octonions. The lowest dimensional even unimodular lattice is the 8-dimensional E8 lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8. A figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating. Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something. 8 (eight) is the natural number following 7 and preceding 9. The SI prefix for 10008 is yotta (Y), and for its reciprocal yocto (y). It is the root of two other numbers: eighteen (eight and ten) and eighty (eight tens). Linguistically, it is derived from Middle English eighte 8 is a composite number, its proper divisors being 1, 2, and 4. It is twice 4 or four times 2. Eight is a power of two, being 23 (two cubed), and is the first number of the form p3. It has an aliquot sum of 7 in the 4 member aliquot sequence (8,7,1,0) being the first member of 7-aliquot tree. It is symbolized by the Arabic numeral (figure) 8. All powers of 2 ;(2x), have an aliquot sum of one less than themselves. Eight is the first number to be the aliquot sum of two numbers other than itself; the discrete biprime 10, and the square number 49. 8 is the base of the octal number system, which is mostly used with computers. In octal, one digit represents 3 bits. In modern computers, a byte is a grouping of eight bits, also called an octet. The number 8 is a Fibonacci number, being 3 plus 5. The next Fibonacci number is 13. 8 is the only Fibonacci number that is a perfect cube.[1] 8 and 9 form a RuthAaron pair under the second definition in which repeated prime factors are counted as often as they occur. A polygon with eight sides is an octagon. Figurate numbers representing octagons (including eight) are called octagonal numbers. A polyhedron with eight faces is an octahedron. A cuboctahedron has as faces six equal squares and eight equal regular triangles. A cube has eight verticies. Sphenic numbers always have exactly eight divisors. 8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra. The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity We also see a period of 8 in the K-theory of spheres and in the representation theory of the rotation groups, the latter giving rise to the 8 by 8 spinorial chessboard. All of these properties are closely related to the properties of the octonions. The lowest dimensional even unimodular lattice is the 8-dimensional E8 lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8. A figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating. Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something.Click Here to Read the rest of the article
