8 (eight) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
7 and preceding
9.
In mathematics
8 is:
* a
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...
, its
proper divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...
s being , , and . It is twice 4 or four times 2.
* a
power of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negative ...
, being 2 (two cubed), and is the first number of the form , being an integer greater than 1.
* the first number which is neither
prime
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
nor
semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime nu ...
.
* the base of the
octal
The octal numeral system, or oct for short, is the radix, base-8 number system, and uses the Numerical digit, digits 0 to 7. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, ...
number system, which is mostly used with
computer
A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...
s. In octal, one digit represents three
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s. In modern computers, a
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
is a grouping of eight bits, also called an
octet
Octet may refer to:
Music
* Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble
** String octet, a piece of music written for eight string instruments
*** Octet (Mendelssohn), 1825 compos ...
.
* a
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
, being plus . The next Fibonacci number is . 8 is the only positive Fibonacci number, aside from 1, that is a perfect cube.
* the only nonzero
perfect power
In mathematics, a perfect power is a natural number that is a product of equal natural factors, or, in other words, an integer that can be expressed as a square or a higher integer power of another integer greater than one. More formally, ''n'' ...
that is one less than another perfect power, by
Mihăilescu's Theorem
Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu at Paderborn University. The integers 23 and 32 are ...
.
* the order of the smallest non-abelian group all of whose subgroups are normal.
* the dimension of the
octonion
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface or blackboard bold \mathbb O. Octonions have e ...
s and is the highest possible dimension of a
normed division algebra
In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. ...
.
* the first number to be the aliquot sum of two numbers other than itself; the discrete biprime , and the square number .
A number is divisible by 8 if its last three digits, when written in
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
, are also divisible by 8, or its last three digits are 0 when written in
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that t ...
.
A
polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...
with eight sides is an
octagon
In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon.
A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...
. The sides and
span
Span may refer to:
Science, technology and engineering
* Span (unit), the width of a human hand
* Span (engineering), a section between two intermediate supports
* Wingspan, the distance between the wingtips of a bird or aircraft
* Sorbitan ester ...
of a
regular octagon
In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon.
A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...
, or
truncated square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...
, are in
silver ratio
In mathematics, two quantities are in the silver ratio (or silver mean) if the ratio of the smaller of those two quantities to the larger quantity is the same as the ratio of the larger quantity to the sum of the smaller quantity and twice t ...
, and its
circumscribing square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...
has a side and diagonal length ratio of ; with both the silver ratio and the
square root of two
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the princip ...
intimately interconnected through
Pell number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , an ...
s, where in particular the quotient of successive Pell numbers generates rational approximations for coordinates of a
regular octagon
In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon.
A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...
. With a
central angle
A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc le ...
of 45 degrees and an
internal angle
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or ) if ...
of 135 degrees, regular octagons are able to
tessellate
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
two-dimensional space alongside squares in the
truncated square tiling
In geometry, the truncated square tiling is a semiregular tiling, semiregular tiling by regular polygons of the Euclidean plane with one square (geometry), square and two octagons on each vertex (geometry), vertex. This is the only edge-to-edge ti ...
, as well as fill a
plane-vertex with a regular
triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, an ...
and a regular
icositetragon
In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees.
Regular icositetragon
The '' regular icositetragon'' is represented by Schläfli symbol ...
. The
Ammann–Beenker tiling
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done independently by F. P. M. Beenker.
Th ...
is a nonperiodic tesselation of
prototile
In the mathematical theory of tessellations, a prototile is one of the shapes of a tile in a tessellation.
Definition
A tessellation of the plane or of any other space is a cover of the space by closed shapes, called tiles, that have disjoint in ...
s that feature prominent octagonal ''silver'' eightfold symmetry, and is the two-dimensional
orthogonal projection
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P=P. That is, whenever P is applied twice to any vector, it gives the same result as if it wer ...
of the
8-8 duoprism. In number theory,
figurate number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean
* polygon ...
s representing octagons are called
octagonal number
An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are
: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 34 ...
s.
A
cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the only r ...
is a
regular polyhedron
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equival ...
with eight
vertices that also forms the
cubic honeycomb
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a re ...
, the only regular honeycomb in three-dimensional space. Through various truncation operations, the
cubic honeycomb
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a re ...
generates eight other
convex uniform honeycombs under the group
. The
octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
, with eight
equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each othe ...
s as
faces
The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affe ...
, is the
dual polyhedron
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. ...
to the cube and one of eight
convex deltahedra. The
stella octangula
The stellated octahedron is the only stellation of the octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers. It was depict ...
, or ''eight-pointed star'', is the only
stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific el ...
with
octahedral symmetry
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the polyhedr ...
. It has eight triangular faces alongside eight vertices that form a cubic
faceting
Stella octangula as a faceting of the cube
In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new Vertex (geometry), vertices.
New edges of a faceted pol ...
, composed of two self-dual
tetrahedra
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
that makes it the simplest of five
regular compound polyhedra. The
cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...
, on the other hand, is a
rectified cube or rectified octahedron, and one of only two convex
quasiregular polyhedra. It contains eight equilateral triangular faces alongside six squares, whose first
stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific el ...
is the
cube-octahedron compound. The
hexagonal prism
In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices..
Since it has 8 faces, it is an octahedron. However, the term ''octahedron'' is primarily used to ...
, which classifies as an
irregular octahedron that is a
parallelohedron
In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedr ...
, like the cube, is able to
tessellate
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
space as a three-dimensional analogue of the
hexagon
In geometry, a hexagon (from Ancient Greek, Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple polygon, simple (non-self-intersecting) hexagon is 720°.
Regular hexa ...
. The
gyrobifastigium
In geometry, the gyrobifastigium is the 26th Johnson solid (). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is the only Johnson solid that can tile ...
, with four square faces and four triangular faces, is the only
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
that is able to tessellate space, while the
truncated octahedron
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagon, hexagons and 6 Squa ...
, also a parallelohedron, is the
permutohedron
In mathematics, the permutohedron of order ''n'' is an (''n'' − 1)-dimensional polytope embedded in an ''n''-dimensional space. Its vertex coordinates (labels) are the permutations of the first ''n'' natural numbers. The edges ident ...
of order four, with eight hexagonal faces alongside six squares that is likewise the only
Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed ...
that can generate a
honeycomb
A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic Beeswax, wax cells built by honey bees in their beehive, nests to contain their larvae and stores of honey and pollen.
beekeeping, Beekee ...
on its own.
Vertex-transitive
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in ...
semiregular polytope
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-transitive and has all its facets being regular polytopes. E.L. Elte compiled a longer list in 1912 as ''The Semiregular Polytop ...
s whose
facets
A facet is a flat surface of a geometric shape, e.g., of a cut gemstone.
Facet may also refer to:
Arts, entertainment, and media
* ''Facets'' (album), an album by Jim Croce
* ''Facets'', a 1980 album by jazz pianist Monty Alexander and his tri ...
are ''finite'' exist up through the 8th dimension. In the
third dimension, they include the
Archimedean solids
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed o ...
and the infinite family of uniform
prisms and
antiprism
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .
Antiprisms are a subclass o ...
s, while in the
fourth dimension, only the
rectified 5-cell
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron and two octahedra. Each vertex has two tetrahedra and three octahedra. In t ...
, the
rectified 600-cell
In geometry, the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge has two octahedra and one icosahedron. Each vertex has five octahedra and two ico ...
, and the
snub 24-cell
In geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra and three icosahedra meet at each vertex. In total it has 480 triangular face ...
are semiregular polytopes. For dimensions
five
5 is a number, numeral, and glyph.
5, five or number 5 may also refer to:
* AD 5, the fifth year of the AD era
* 5 BC, the fifth year before the AD era
Literature
* ''5'' (visual novel), a 2008 visual novel by Ram
* ''5'' (comics), an awa ...
through eight, the
demipenteract
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a ''5-hypercube'' (penteract) with alternated vertices removed.
It was discovered by Thorold Gosset. Since it was the only semiregular 5- ...
and the
k21 polytopes 221,
321, and
421 are the only semiregular (
Gosset) polytopes. Collectively, the k
21 family of polytopes contains eight figures that are rooted in the
triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is ''oblique''. A unif ...
, which is the simplest semiregular polytope that is made of three cubes and two equilateral triangles. It also includes one of only three semiregular
Euclidean honeycombs: the
affine
Affine may describe any of various topics concerned with connections or affinities.
It may refer to:
* Affine, a relative by marriage in law and anthropology
* Affine cipher, a special case of the more general substitution cipher
* Affine comb ...
521 honeycomb that represents the arrangement of vertices of the eight-dimensional
lattice, and made of 4
21 facets
A facet is a flat surface of a geometric shape, e.g., of a cut gemstone.
Facet may also refer to:
Arts, entertainment, and media
* ''Facets'' (album), an album by Jim Croce
* ''Facets'', a 1980 album by jazz pianist Monty Alexander and his tri ...
. The culminating figure is the ninth-dimensional
621 honeycomb, which is the only affine semiregular
paracompact
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, ...
hyperbolic
Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry.
The following phenomena are described as ''hyperbolic'' because they ...
honeycomb with infinite facets and
vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
Definitions
Take some corner or Vertex (geometry), vertex of a polyhedron. Mark a point somewhere along each connect ...
s in the k
21 family. There are no other finite semiregular polytopes or honeycombs in dimensions ''n'' > 8.
Sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
s always have exactly eight divisors.
The number 8 is involved with a number of interesting mathematical phenomena related to the notion of
Bott periodicity
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by , which proved to be of foundational significance for much further research, in particular in K-theory of stable comple ...
. If
is the direct limit of the inclusions of real orthogonal groups
, the following holds:
:
.
Clifford algebras also display a periodicity of 8. For example, the algebra ''Cl''(''p'' + 8,''q'') is isomorphic to the algebra of 16 by 16 matrices with entries in ''Cl''(''p'',''q''). We also see a period of 8 in the
K-theory
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, ...
of spheres and in the
representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
of the
rotation groups, the latter giving rise to the 8 by 8
spinor
In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight ...
ial chessboard. All of these properties are closely related to the properties of the
octonion
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface or blackboard bold \mathbb O. Octonions have e ...
s.
The
spin group
In mathematics the spin group Spin(''n'') page 15 is the double cover of the special orthogonal group , such that there exists a short exact sequence of Lie groups (when )
:1 \to \mathrm_2 \to \operatorname(n) \to \operatorname(n) \to 1.
As a L ...
Spin(8) is the unique such group that exhibits the phenomenon of
triality
In mathematics, triality is a relationship among three vector spaces, analogous to the duality relation between dual vector spaces. Most commonly, it describes those special features of the Dynkin diagram D4 and the associated Lie group Spin(8) ...
.
The lowest-dimensional even
unimodular lattice
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in ''n''-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamen ...
is the 8-dimensional
lattice. Even positive definite unimodular lattices exist only in dimensions divisible by 8.
A figure 8 is the common name of a
geometric
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
shape
A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type.
A pl ...
, 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.
List of basic calculations
Etymology
English ''eight'', from Old English ''eahta, æhta'',
Proto-Germanic
Proto-Germanic (abbreviated PGmc; also called Common Germanic) is the reconstructed proto-language of the Germanic branch of the Indo-European languages.
Proto-Germanic eventually developed from pre-Proto-Germanic into three Germanic branc ...
''*ahto''
is a direct continuation of
Proto-Indo-European
Proto-Indo-European (PIE) is the reconstructed common ancestor of the Indo-European language family. Its proposed features have been derived by linguistic reconstruction from documented Indo-European languages. No direct record of Proto-Indo-E ...
''
*oḱtṓ(w)-'', and as such cognate with Greek and Latin ''octo-'', both of which stems are reflected by the English prefix
oct(o)-, as in the ordinal adjective ''octaval'' or ''octavary'', the distributive adjective is ''
octonary : ''For the base-8 numeral system, see octal.''
An octonary is an eight-line section in a poem, song or psalm. The most notable example is found in Psalm 119Calvin ''Bible Commentaries: Psalms, Part IV'' p287 "Some call this the octonary psalm, bec ...
''.
The adjective ''octuple'' (Latin ''octu-plus'') may also be used as a noun, meaning "a set of eight items"; the diminutive ''
octuplet
A multiple birth is the culmination of one multiple pregnancy, wherein the mother gives birth to two or more babies. A term most applicable to vertebrate species, multiple births occur in most kinds of mammal
Mammals () are a group of ...
'' is mostly used to refer to eight siblings delivered in one birth.
The
Semitic numeral is based on a root ''*θmn-'', whence Akkadian ''smn-'', Arabic ''ṯmn-'', Hebrew ''šmn-'' etc.
The
Chinese numeral
Chinese numerals are words and characters used to denote numbers in Chinese.
Today, speakers of Chinese use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous sy ...
, written (
Mandarin
Mandarin or The Mandarin may refer to:
Language
* Mandarin Chinese, branch of Chinese originally spoken in northern parts of the country
** Standard Chinese or Modern Standard Mandarin, the official language of China
** Taiwanese Mandarin, Stand ...
: ''bā'';
Cantonese
Cantonese ( zh, t=廣東話, s=广东话, first=t, cy=Gwóngdūng wá) is a language within the Chinese (Sinitic) branch of the Sino-Tibetan languages originating from the city of Guangzhou (historically known as Canton) and its surrounding are ...
: ''baat''), is from
Old Chinese
Old Chinese, also called Archaic Chinese in older works, is the oldest attested stage of Chinese language, Chinese, and the ancestor of all modern varieties of Chinese. The earliest examples of Chinese are divinatory inscriptions on oracle bones ...
''*priāt-'', ultimately from Sino-Tibetan
''b-r-gyat'' or ''b-g-ryat'' which also yielded Tibetan ''
brgyat''.
It has been argued that, as the
cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. Th ...
is the highest number of items that can universally be
cognitively processed as a single set, the etymology of the numeral ''eight'' might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar.
The
Turkic words for "eight" are from a
Proto-Turkic
Proto-Turkic is the linguistic reconstruction of the common ancestor of the Turkic languages that was spoken by the Proto-Turks before their divergence into the various Turkic peoples. Proto-Turkic separated into Oghur (western) and Common Turk ...
stem ''*sekiz'', which has been suggested as originating as a negation of ''eki'' "two", as in "without two fingers" (i.e., "two short of ten; two fingers are not being held up");
this same principle is found in
Finnic ''
*kakte-ksa'', which conveys a meaning of "two before (ten)". The Proto-Indo-European reconstruction ''
*oḱtṓ(w)-'' itself has been argued as representing an old dual, which would correspond to an original meaning of "twice four".
Proponents of this "quaternary hypothesis" adduce the numeral ', which might be built on the stem ''new-'', meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight).
Evolution of the Arabic digit
![Evo8glyph](https://upload.wikimedia.org/wikipedia/commons/9/93/Evo8glyph.svg)
The modern digit 8, like all modern
Arabic numerals
Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write Decimal, decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers ...
other than zero, originates with the
Brahmi numerals
The Brahmi numerals are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are a non positional decimal system. They are the direct graphic ancestors of the modern Hindu–Arabic numeral s ...
.
The Brahmi digit for ''eight'' by the 1st century was written in one stroke as a curve └┐ looking like an uppercase H with the bottom half of the left line and the upper half of the right line removed.
However, the digit for eight used in India in the early centuries of the Common Era developed considerable graphic variation, and in some cases took the shape of a single wedge, which was adopted into the Perso-Arabic tradition as
٨ (and also gave rise to the later Devanagari form
८); the alternative curved glyph also existed as a variant in Perso-Arabic tradition, where it came to look similar to our digit 5.
The digits as used in
Al-Andalus
Al-Andalus DIN 31635, translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label=Berber languages, Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, ...
by the 10th century were a distinctive western variant of the glyphs used in the Arabic-speaking world, known as ''ghubār'' numerals (''ghubār'' translating to "
sand table
A sand table uses constrained sand for modelling or educational purposes. The original version of a sand table may be the abax used by early Greek students. In the modern era, one common use for a sand table is to make terrain models for milita ...
"). In these digits, the line of the ''5''-like glyph used in Indian manuscripts for eight came to be formed in ghubār as a closed loop, which was the ''8''-shape that became adopted into European use in the 10th century.
Just as in most modern
typeface
A typeface (or font family) is the design of lettering that can include variations in size, weight (e.g. bold), slope (e.g. italic), width (e.g. condensed), and so on. Each of these variations of the typeface is a font.
There are list of type ...
s, in typefaces with
text figures
Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...
the character for the digit 8 usually has an
ascender, as, for example, in .
The
infinity symbol
The infinity symbol (\infty) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves of a similar shape studied in algebraic geometry, or "lazy eight", in the terminol ...
∞, described as a "sideways figure eight", is unrelated to the digit 8 in origin; it is first used (in the mathematical meaning "infinity") in the 17th century, and it may be derived from the
Roman numeral
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
for "one thousand" CIƆ, or alternatively from the final Greek letter,
ω.
In science
Physics
* In nuclear physics, the second
magic number.
* In
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, the
eightfold way is used to classify sub-atomic particles.
* In
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
, the
eight-vertex model
In statistical mechanics, the eight-vertex model is a generalisation of the ice-type (six-vertex) models; it was discussed by Sutherland, and Fan & Wu, and solved by Baxter in the zero-field case.
Description
As with the ice-type models, the ei ...
has 8 possible configurations of arrows at each vertex.
Astronomy
*
Messier object
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters'').
Because Messier was only int ...
Lagoon Nebula, M8, a magnitude 5.0 nebula in the constellation of Sagittarius (constellation), Sagittarius.
* The New General Catalogue]
objectNGC 8, a double star in the constellation Pegasus (constellation), Pegasus.
* Since the demotion of Pluto to a dwarf planet on 24 August 2006, in our Solar System, eight of the bodies orbiting the Sun are considered to be planets.
Chemistry
* The atomic number of oxygen.
* The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.
* The maximum number of electrons that can occupy a electron shell#Valence shells, valence shell.
* The red pigment lycopene consists of eight isoprene units.
Geology
* A disphenoid crystal is bounded by eight scalene triangles arranged in pairs. A ditetragonal prism in the tetragonal crystal system has eight similar faces whose alternate interfacial angles only are equal.
Biology
* All spiders, and more generally all arachnids, have eight legs. Orb-weaver spiders of the cosmopolitan family Areneidae have eight similar eyes.
* The octopus and its cephalopod relatives in genus Argonaut (animal), ''Argonauta'' have eight arms (tentacles).
* Compound coelenterates of the subclass or order octocorallia, Alcyonaria have polyps with eight-branched tentacles and eight septa.
* Sea anemones of genus ''Edwardsia'' have eight Mesentery#Invertebrate anatomy, mesenteries.
* Animals of phylum Ctenophora swim by means of eight meridional bands of transverse ciliated plates, each plate representing a row of large modified cilia.
* The Alypia octomaculata, eight-spotted forester (genus ''Alypia'', family Zygaenidae) is a diurnal moth having black wings with brilliant white spots.
* The ascus in fungi of the class Ascomycota#Ascomycetes versus Ascomycetes, Ascomycetes, following nuclear fusion, bears within it typically eight ascospores.
* Herbs of genus ''Coreopsis'' (tickseed) have showy flower heads with involucral bracts in two distinct series of eight each.
* In human adult dentition there are eight teeth in each quadrant. The eighth tooth is the so-called wisdom tooth.
* There are eight cervical nerves on each side in man and most mammals.
Psychology
* There are eight Jungian cognitive functions, according to the MBTI models by John Beebe and Linda Berens.
* Timothy Leary identified a 8-Circuit Model of Consciousness, hierarchy of eight levels of consciousness.
In technology
* A
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
is eight
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s.
* Many (mostly historic) computer architectures are eight-bit, among them the Nintendo Entertainment System.
* Standard 8 mm film, Standard-8 and Super 8 mm film, Super-8 are 8 mm List of film formats, film formats.
* Video8, Hi8 and Digital8 are related 8 mm video formats.
* On most phones, the 8 key is associated with the letters T, U, and V, but on the BlackBerry Pearl it is the key for B and N.
* An eight may refer to an eight-cylinder engine or automobile. A V8 engine is an internal combustion engine with eight cylinders configured in two banks (rows) of four forming a "V" when seen from the end.
* A figure-eight knot (so named for its configuration) is a kind of stopper knot.
* The number eight written in parentheses is the code for the musical note in Windows Live Messenger.
* In a seven-segment display, when an 8 is illuminated, all the display bulbs are on.
In measurement
* The SI prefix for 1000
8 is yotta (Y), and for its reciprocal, yocto (y).
* In liquid measurement (United States customary units), there are eight fluid ounces in a Cup (volume), cup, eight pints in a gallon and eight tablespoonfuls in a gill (volume), gill.
* There are eight furlongs in a mile.
* The clove, an old English units#Avoirdupois, English unit of weight, was equal to eight pounds when measuring cheese.
* An eight may be an article of clothing of the eighth clothing sizes, size.
* Force eight is the first wind strength attributed to a gale on the Beaufort scale when announced on a Shipping Forecast.
In culture
Currency
* Sailors and civilians alike from the 1500s onward referred to evenly divided parts of the Spanish dollar as "pieces of eight", or "bits".
Architecture
* Various types of buildings are usually eight-sided (octagonal), such as single-roomed gazebos and multi-roomed pagodas (descended from stupas; see religion section below).
* Eight Glossary of architecture#C, caulicoles rise out of the leafage in a Corinthian order, Corinthian capital, ending in leaves that support the volutes.
In religion, folk belief and divination
Hinduism
* Also known as Ashtha, Aṣṭa, or Ashta in Sanskrit, it is the number of wealth and abundance.
* The goddess of wealth and prosperity, Lakshmi, has eight forms known as Ashta Lakshmi and worshipped as:
"''Maha-lakshmi, Dhana-lakshmi, Dhanya-lakshmi, Gaja-lakshmi,
Santana-lakshmi, Veera-lakshmi, Vijaya-lakshmi and Vidhya-lakshmi''"
*There are eight ''nidhi'', or seats of wealth, according to Hinduism.
*There are eight guardians of the directions known as ''Astha-dikpalas''.
*There are eight Hindu monasteries established by the saint Madhvacharya in Udupi, India popularly known as the ''Ashta Mathas of Udupi''.
Buddhism
* The Dharmacakra, a Buddhism, Buddhist symbol, has eight spokes. The Buddha's principal teaching—the Four Noble Truths—ramifies as the Noble Eightfold Path and the Buddha emphasizes the importance of the eight attainments or jhanas.
* In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas: (Manjusri, Vajrapani, Avalokiteśvara, Maitreya, Ksitigarbha, Nivaranavishkambhi, Akasagarbha, and Samantabhadra (Bodhisattva), Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogacara school of thought: consciousness in the five senses, thought-consciousness, self-consciousness, and unconsciousness-"consciousness" or "store-house consciousness" (alaya-vijñana). The "irreversible" state of enlightenment, at which point a Bodhisattva goes on "autopilot", is the Eight Ground or ''bhūmi''. In general, "eight" seems to be an auspicious number for Buddhists, e.g., the "eight auspicious symbols" (the jewel-encrusted parasol; the goldfish (always shown as a pair, e.g., the glyph of Pisces); the self-replenishing amphora; the white ''kamala'' lotus-flower; the white conch; the eternal (Celtic-style, infinitely looping) knot; the banner of imperial victory; the eight-spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching). Similarly, Buddha's Birthday, Buddha's birthday falls on the 8th day of the 4th month of the Chinese calendar.
Judaism
* The religious rite of brit milah (commonly known as circumcision) is held on a baby boy's eighth day of life.
* Hanukkah is an eight-day Jewish holiday that starts on the 25th day of Kislev.
* Shemini Atzeret (Hebrew language, Hebrew: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of Sukkot.
Christianity
* The spiritual The eighth day (Christian), Eighth Day, because the number 7 refers to the days of the week (which repeat themselves).
* The number of Beatitudes.
* wikisource:Bible (King James)/1 Peter#3:20, 1 Peter 3:20 states that there were eight people on Noah's Ark.
* The Antichrist is the eighth king in the Book of Revelation.
Islam
* In Islam, eight is the number of angels carrying the Throne of God, throne of Allah in heaven.
* The number of gates of heaven
Taoism
* Ba Gua
* Ba Xian
* baduanjin, Ba Duan Jin
Other
* In Wicca, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year.
* In Ancient Egyptian mythology, the Ogdoad (Egyptian), Ogdoad represents the Ancient Egyptian creation myths, eight primordial deities of creation.
* In Scientology there are eight dynamics of existence.
* There is also the Ogdoad (Gnosticism), Ogdoad in Gnosticism.
As a lucky number
* The number eight is considered to be a Numbers in Chinese culture, lucky number in Chinese and other Asian cultures. Eight (; Chinese numerals#Numeral characters, accounting ; pinyin ''bā'') is considered a Numbers in Chinese culture#Eight, lucky number in Chinese culture because it sounds like the word meaning to generate wealth (; Pinyin: ''fā''). Property with the number 8 may be valued greatly by Chinese. For example, a Hong Kong Vehicle registration plate, number plate with the number 8 was sold for $640,000. The opening ceremony of the 2008 Summer Olympics, Summer Olympics in Beijing started at 8 seconds and 8 minutes past 8 pm (local time) on 8 August 2008.
* In Pythagorean numerology (a pseudoscience) the number 8 represents victory, prosperity and overcoming.
* is also considered a lucky number in Japan, but the reason is different from that in Chinese culture. Eight gives an idea of growing prosperous, because the letter () broadens gradually.
* The Japanese thought of as a holy number in the ancient times. The reason is less well-understood, but it is thought that it is related to the fact they used eight to express large numbers vaguely such as (literally, eightfold and twentyfold), (literally, eight clouds), (literally, eight millions of Gods), etc. It is also guessed that the ancient Japanese gave importance to pairs, so some researchers guess twice as , which is also guessed to be a holy number in those times because it indicates the world (north, south, east, and west) might be considered a very holy number.
* In numerology, 8 is the number of building, and in some theories, also the number of destruction.
In astrology
* In astrology, Scorpius, Scorpio is the 8th astrological sign of the Zodiac.
* In the Middle Ages, 8 was the number of "unmoving" stars in the sky, and symbolized the perfection of incoming planetary energy.
In music and dance
* A note played for one-eighth the duration of a whole note is called an eighth note, or quaver.
* An octave, the interval between two musical notes with the same letter name (where one has double the frequency of the other), is so called because there are eight notes between the two on a standard major or minor diatonic scale, including the notes themselves and without chromatic deviation. The ecclesiastical musical mode, modes are ascending diatonic musical scales of eight notes or tones comprising an octave.
* There are eight notes in the octatonic scale.
* There are eight musicians in a double quartet or an octet (music), octet. Both terms may also refer to a musical composition for eight voices or instruments.
* Caledonians is a square dance for eight, resembling the quadrille.
* Albums with the number eight in their title include ''8'' by the Swedish band Arvingarna, ''8 (Incubus album), 8'' by the American rock band Incubus (band), Incubus, ''The Meaning of 8'' by Minnesota indie rock band Cloud Cult and ''8ight'' by Anglo-American singer-songwriter Beatie Wolfe.
* Dream Theater's eighth album ''Octavarium (album), Octavarium'' contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork.
* "Eight maids a-milking" is the gift on the eighth day of Christmas in the carol "The Twelve Days of Christmas (song), The Twelve Days of Christmas".
* The 8-track tape, 8-track cartridge is a musical recording format.
* "#8" is the stage name of Slipknot (band), Slipknot vocalist Corey Taylor.
* "Too Many Eights" is a song by Athens, Georgia's Supercluster (band), Supercluster.
* Eight Seconds, a Canadian musical group popular in the 1980s with their most notable song "Kiss You (When It's Dangerous)".
* "Eight Days a Week (song), Eight Days a Week" is a #1 single for the music group The Beatles.
* Figure 8 (album), ''Figure 8'' is the fifth studio album by singer-songwriter Elliott Smith, released in the year 2000, an album released by Julia Darling in 1999, and an album released by Outasight in 2011.
* Ming Hao from the k-pop group Seventeen (South Korean band)#Performance team, Seventeen goes by the name "The8".
* "8 (circle)" is the eighth song on the album ''22, A Million'' by the American band Bon Iver.
* "8" is the eighth song on the album ''When We All Fall Asleep, Where Do We Go?'' by Billie Eilish.
In film and television
* ''8 Guys'' is a 2003 short film written and directed by Dane Cook.
* ''8 Man'' (or ''Eightman''): 1963 Japanese manga and anime superhero.
* 8 Mile (film), ''8 Mile'' is a 2002 film directed by Curtis Hanson.
* 8mm (film), ''8 mm'' is a 1999 film directed by Joel Schumacher.
* ''8 Women'' (Original French title: ) is a 2001 film directed by François Ozon.
* ''Eight Below'' is a 2006 film directed by Frank Marshall (film producer), Frank Marshall.
* ''Eight Legged Freaks'' is a 2002 film directed by Ellory Elkayem.
* ''Eight Men Out'' is a 1988 film directed by John Sayles.
* ''Jennifer Eight'', also known as ''Jennifer 8'', is a 1992 film written and directed by Bruce Robinson.
* ''Eight Is Enough'' is an American television comedy-drama series.
* In ''Stargate SG-1'' and ''Stargate Atlantis'', dialing an 8-chevron address will open a wormhole to another galaxy.
* ''The Hateful Eight'' is a 2015 American western mystery film written and directed by Quentin Tarantino.
* ''Kate Plus 8'' is an American reality television show.
In sports and other games
* Eight-ball pool (cue sports), pool is played with a cue ball and 15 numbered balls, the black ball numbered 8 being the middle and most important one, as the winner is the player or side that legally pockets it after first pocketing its numerical group of 7 object balls (for other meanings see ''Eight ball (disambiguation)'').
* In chess, each side has eight pawns and the board is made of 64 squares arranged in an eight by eight lattice. The eight queens puzzle is a challenge to arrange eight queens on the board so that none can capture any of the others.
* In the game of eights or Crazy Eights, each successive player must play a card either of the same suit or of the same rank as that played by the preceding player, or may play an eight and call for any suit. The object is to get rid of all one's cards first.
* In association football, the number 8 has historically been the number of the Central Midfielder.
* In Australian rules football, the top eight teams at the end of the Australian Football League regular season qualify for the AFL finals series, finals series (i.e. playoffs).
* In baseball:
** The center fielder is designated as number 8 for scorekeeping purposes.
** The College World Series, the final phase of the NCAA Division I Baseball Championship, NCAA Division I tournament, features eight teams.
* In rugby union, the only position without a proper name is the Number eight (rugby union), Number 8, a forward position.
* In rugby league:
** Most competitions (though not the Super League, which uses static squad numbering) use a position-based player numbering system in which one of the two starting props wears the number 8.
** The Australia-based National Rugby League has its own 8-team finals series, similar but not identical in structure to that of the Australian Football League.
* In Rowing (sport), rowing, an "eight" refers to a sweep-oar racing boat with a crew of eight rowers plus a coxswain.
* In the 2008 Summer Olympics, 2008 Games of the XXIX Olympiad held in Beijing, the official opening was on 08/08/08 at 8:08:08 p.m. China Standard Time, CST.
* In Rock Climbing, climbers frequently use the Figure-eight knot, Figure Eight knot to tie into their harnesses.
In foods
* Nestlé sells a brand of chocolates filled with peppermint-flavoured cream called After Eight, referring to the time 8 p.m.
* There are eight vegetables in V8 (beverage), V8 juice.
In literature
* Eights may refer to octosyllable, octosyllabic, usually Choliamb, iambic, Meter (poetry), lines of verse.
* The drott-kvaett, an Old Icelandic verse, consisted of a stanza of eight regular lines.
* In Terry Pratchett's ''Discworld'' series, eight is a magical number and is considered taboo. Eight is not safe to be said by wizards on the Discworld (world), Discworld and is the number of Bel-Shamharoth. Also, there are eight days in a Disc week and eight colours in a Disc spectrum, the eighth one being octarine.
* Lewis Carroll's poem ''The Hunting of the Snark'' has 8 "fits" (cantos), which is noted in the full name "The Hunting of the Snark – ''An Agony, in Eight Fits''."
* Eight apparitions appear to Macbeth (character), Macbeth in Act 4 scene 1 of Shakespeare's ''Macbeth'' as representations of the eight descendants of Banquo.
In slang
* An "eighth" is a common measurement of cannabis (drug), marijuana, meaning an eighth of an ounce. It is also a common unit of sale for psilocybin mushrooms.
* Avril Lavigne's song "Sk8er Boi" uses this convention in the title.
* "Section 8" is common U.S. slang for "crazy", based on the United States armed forces, U.S. military's Section 8 (military), Section 8 discharge for Mental disorder, mentally unfit personnel.
* The Section 8 (housing), Housing Choice Voucher Program, operated by the United States Department of Housing and Urban Development, is commonly referred to as the Section 8 program, as this was the original section of the Act which instituted the program.
* In Colombia and Venezuela, "volverse un ocho" (meaning to tie oneself in a figure 8) refers to getting in trouble or contradicting oneself.
* In China, "8" is used in chat speak as a term for parting. This is due to the closeness in pronunciation of "8" (bā) and the English word "bye".
See also
* The Magical Number Seven, Plus or Minus Two
*List of highways numbered 8
References
External links
The Octonions John C. Baez
{{DEFAULTSORT:8 (Number)
Integers
8 (number)