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4 (four) is a
number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
, numeral and digit. It 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 3 and preceding 5. It is the smallest
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 ...
and
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, ...
, and is considered unlucky in many East Asian cultures.


In mathematics

Four is the smallest
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 . Four is the sum and product of
two 2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultur ...
with itself: 2 + 2 = 4 = 2 x 2, the only number b such that a + a = b = a x a, which also makes four the smallest squared
prime number 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 ...
p^. In
Knuth's up-arrow notation In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperati ...
, , and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically
three 3 is a number, numeral, and glyph. 3, three, or III may also refer to: * AD 3, the third year of the AD era * 3 BC, the third year before the AD era * March, the third month Books * '' Three of Them'' (Russian: ', literally, "three"), a 1901 ...
. The sum of the first four prime numbers
two 2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultur ...
+
three 3 is a number, numeral, and glyph. 3, three, or III may also refer to: * AD 3, the third year of the AD era * 3 BC, the third year before the AD era * March, the third month Books * '' Three of Them'' (Russian: ', literally, "three"), a 1901 ...
+
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 ...
+
seven 7 is a number, numeral, and glyph. 7 or seven may also refer to: * AD 7, the seventh year of the AD era * 7 BC, the seventh year before the AD era * The month of July Music Artists * Seven (Swiss singer) (born 1978), a Swiss recording artist ...
is the only sum of four consecutive prime numbers that yields an
odd Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: Acronym * ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...
prime number,
seventeen Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese m ...
, which is the fourth
super-prime Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins :3, 5, 11, 17, 31, ...
. Four lies between the first proper pair of
twin primes A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...
,
three 3 is a number, numeral, and glyph. 3, three, or III may also refer to: * AD 3, the third year of the AD era * 3 BC, the third year before the AD era * March, the third month Books * '' Three of Them'' (Russian: ', literally, "three"), a 1901 ...
and
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 ...
, which are the first two
Fermat prime In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 4294967 ...
s, like
seventeen Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese m ...
, which is the third. On the other hand, the
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 ...
of four 42, equivalently the
fourth power In arithmetic and algebra, the fourth power of a number ''n'' is the result of multiplying four instances of ''n'' together. So: :''n''4 = ''n'' × ''n'' × ''n'' × ''n'' Fourth powers are also formed by multiplying a number by its cube. Further ...
of two 24, is sixteen; the only number that has a^ = b^ as a form of
factorization In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a p ...
. Holistically, there are four elementary arithmetic operations in mathematics:
addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol ) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication and Division (mathematics), division. ...
(+),
subtraction Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...
(−),
multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...
(×), and
division Division or divider may refer to: Mathematics *Division (mathematics), the inverse of multiplication *Division algorithm, a method for computing the result of mathematical division Military *Division (military), a formation typically consisting ...
(÷); and four basic
number system A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
s, the
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
s \mathbb,
rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...
s \mathbb,
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
s \mathbb, and
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 ...
s \mathbb. Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y^z^. A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because .
Lagrange's four-square theorem Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four. p = a_0^2 + a_1^2 + a_2^2 + a_ ...
states that every positive integer can be written as the sum of at most four
square number In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals ...
s. Three are not always sufficient; for instance cannot be written as the sum of three squares. There are four
all-Harshad number In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad number ...
s: 1, 2, ''4'', and 6. 12, which is divisible by four thrice over, is a Harshad number in all bases except
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, ...
. A four-sided plane figure is a
quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
or quadrangle, sometimes also called a ''tetragon''. It can be further classified as a
rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containi ...
or ''oblong'',
kite A kite is a tethered heavier than air flight, heavier-than-air or lighter-than-air craft with wing surfaces that react against the air to create Lift (force), lift and Drag (physics), drag forces. A kite consists of wings, tethers and anchors. ...
,
rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...
, and
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 ...
. Four is the highest degree general
polynomial equation In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term ''algebraic equation' ...
for which there is a
solution in radicals A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, divi ...
. The
four-color theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...
states that a
planar graph In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross ...
(or, equivalently, a flat
map A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...
of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors. Three colors are not, in general, sufficient to guarantee this. The largest planar
complete graph In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is c ...
has four vertices. A solid figure with four faces as well as four vertices is a
tetrahedron 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 ...
, which is the smallest possible number of faces and vertices a
polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on th ...
can have. The regular tetrahedron, also called a 3-
simplex In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
, is the simplest
Platonic solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
. It has four
regular 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 that are themselves at dual positions with the vertices of another tetrahedron. Tetrahedra can be inscribed inside all other four Platonic solids, and tessellate space alongside the
regular 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 ...
in the
alternated cubic honeycomb The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2. Other names incl ...
.
Four-dimensional space A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...
is the highest-dimensional space featuring more than three regular
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope ...
figures: *Two-dimensional: infinitely many
regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either convex p ...
s. *Three-dimensional: five
regular polyhedra 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 ...
; the five
Platonic solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
s which are the
tetrahedron 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 ...
,
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 ...
,
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 ...
,
dodecahedron In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
, and
icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
. *Four-dimensional: six
regular polychora In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regu ...
; the
5-cell In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It i ...
, 8-cell or
tesseract In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eig ...
,
16-cell In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mi ...
,
24-cell In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called C24, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, oct ...
,
120-cell In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called a C120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, heca ...
, and
600-cell In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also known as the C600, hexacosichoron and hexacosihedroid. It is also called a tetraplex (abbreviated from " ...
. The
24-cell In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called C24, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, oct ...
, made of regular
octahedra 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 ...
, has no analogue in any other dimension; it is
self-dual In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a Injective function, one-to-one fashion, often (but not always) by means of an Involution (mathematics), involutio ...
, with its
24-cell honeycomb In Four-dimensional space, four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular polytope, regular space-filling tessellation (or honeycomb (geometry), honeycomb) of 4-dimensional Euclidean space by ...
dual to the
16-cell honeycomb In Four-dimensional space, four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycomb (geometry), honeycombs), represented by Schläfli symbol , and constructed by a 4-dimensiona ...
. *Five-dimensional and every higher dimension: three regular convex n-
polytope In elementary geometry, a polytope is a geometric object with flat sides (''faces''). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an -d ...
s, all within the infinite family of regular n-
simplex In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
es, n-
hypercube In geometry, a hypercube is an ''n''-dimensional analogue of a square () and a cube (). It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, ...
s, and n- orthoplexes. The fourth dimension is also the highest dimension where regular self-intersecting figures exist: *Two-dimensional: infinitaly many regular
star polygon In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations ...
s. *Three-dimensional: ''four'' regular
star polyhedra In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: *Polyhedra which self-intersect in a repetitive way. *Concave p ...
, the regular Kepler-Poinsot star polyhedra. *Four-dimensional: ten regular star polychora, the Schläfli–Hess star polychora. They contain
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
of Kepler-Poinsot polyhedra alongside regular tetrahedra,
icosahedra In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
and
dodecahedra In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
. *Five-dimensional and every higher dimension: zero regular star-polytopes;
uniform A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...
star polytopes in dimensions n > 4 are the most symmetric, which mainly originate from
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 ...
s of regular n-polytopes. Altogether, sixteen (or 16 = 42) regular convex and star polychora are generated from symmetries of ''four'' (4)
Coxeter Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century. Biography Coxeter was born in Kensington to ...
Weyl group In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections th ...
s and
point groups In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every p ...
in the fourth dimension: the \mathrm A_ simplex, \mathrm B_ hypercube, \mathrm F_ icositetrachoric, and \mathrm H_ hexacosichoric groups; with the \mathrm D_
demihypercube In geometry, demihypercubes (also called ''n-demicubes'', ''n-hemicubes'', and ''half measure polytopes'') are a class of ''n''-polytopes constructed from alternation of an ''n''-hypercube, labeled as ''hγn'' for being ''half'' of the hype ...
group generating two alternative constructions. There are also sixty-four (or 64 = 43) four-dimensional
Bravais lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_ ...
s, ''and'' sixty-four
uniform polychora In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons. There are 47 non-prismatic convex uniform 4-polytopes. There ...
in the fourth dimension based on the same \mathrm A_, \mathrm B_, \mathrm F_ and \mathrm H_
Coxeter groups In mathematics, a Coxeter group, named after Harold Scott MacDonald Coxeter, H. S. M. Coxeter, is an group (mathematics), abstract group that admits a group presentation, formal description in terms of Reflection (mathematics), reflections (or Kal ...
, and extending to prismatic groups of
uniform polyhedra In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fa ...
, including one special non-Wythoffian form, the
grand antiprism In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra. It is an anomalous, non-Wythoffian uniform 4-polytope ...
. There are also two infinite families of
duoprism In geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an -polytope and an -polytope is an -polytope, wher ...
s and antiprismatic prisms in the fourth dimension. Four-dimensional
differential manifold In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One ma ...
s have some unique properties. There is only one
differential structure In mathematics, an ''n''-dimensional differential structure (or differentiable structure) on a set ''M'' makes ''M'' into an ''n''-dimensional differential manifold, which is a topological manifold with some additional structure that allows for diff ...
on \mathbb^n except when n = 4, in which case there are uncountably many. The smallest non-
cyclic group In group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted C''n'', that is generated by a single element. That is, it is a set of invertible elements with a single associative bina ...
has four elements; it is the
Klein four-group In mathematics, the Klein four-group is a Group (mathematics), group with four elements, in which each element is Involution (mathematics), self-inverse (composing it with itself produces the identity) and in which composing any two of the three ...
. ''A''
alternating group In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted by or Basic prop ...
s are not
simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnn ...
for values n4. Further extensions of the real numbers under Hurwitz's theorem states that there are four normed division algebras: the real numbers \mathbb, the
complex numbers In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...
\mathbb C, the
quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quatern ...
s \mathbb H, and 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 \mathbb O. Under
Cayley–Dickson construction In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by ...
s, the
sedenion In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers; they are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic to ...
s \mathbb S constitute a further fourth extension over \mathbb. The real numbers are ordered,
commutative In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name o ...
and
associative In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement f ...
algebras In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition a ...
, as well as
alternative algebra In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have *x(xy) = (xx)y *(yx)x = y(xx) for all ''x'' and ''y'' in the algebra. Every associative algebra is ...
s with
power-associativity In mathematics, specifically in abstract algebra, power associativity is a property of a binary operation that is a weak form of associativity. Definition An algebra over a field, algebra (or more generally a magma (algebra), magma) is said to be ...
. The complex numbers \mathbb C share all four multiplicative algebraic properties of the reals \mathbb, without being ordered. The quaternions loose a further commutative algebraic property, while holding associative, alternative, and power-associative properties. The octonions are alternative and power-associative, while the sedenions are only power-associative. The sedenions and all further ''extensions'' of these four normed division algebras are solely power-associative with non-trivial
zero divisor In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero in such that , or equivalently if the map from to that sends to is not injective. Similarly, an element of a ring is called a right zero ...
s, which makes them non-division algebras. \mathbb has a
vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can ...
of
dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
1, while \mathbb C, \mathbb H, \mathbb O and \mathbb S work in
algebraic number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a f ...
s of dimensions 2, 4, 8, and 16, respectively.


List of basic calculations


Evolution of the Hindu-Arabic digit

Brahmic 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 ...
represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The
Shunga is a type of Japanese erotic art typically executed as a kind of ukiyo-e, often in woodblock print format. While rare, there are also extant erotic painted handscrolls which predate ukiyo-e. Translated literally, the Japanese word ''shunga'' ...
would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern. The
Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...
s' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the digit less cursive, ending up with a digit very close to the original Brahmin cross. While the shape of the character for the digit 4 has an ascender 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 glyph usually has a
descender In typography and handwriting, a descender is the portion of a letter that extends below the baseline of a font. For example, in the letter ''y'', the descender is the "tail", or that portion of the diagonal line which lies below the ''v'' c ...
, as, for example, in . On the
seven-segment display A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays. Seven-segment displays are widely used in digital clocks, electronic meters, basic ...
s of pocket calculators and digital watches, as well as certain
optical character recognition Optical character recognition or optical character reader (OCR) is the electronic or mechanical conversion of images of typed, handwritten or printed text into machine-encoded text, whether from a scanned document, a photo of a document, a scen ...
fonts, 4 is seen with an open top.
Television station A television station is a set of equipment managed by a business, organisation or other entity, such as an amateur television (ATV) operator, that transmits video content and audio content via radio waves directly from a transmitter on the earth ...
s that operate on
channel 4 Channel 4 is a British free-to-air public broadcast television network operated by the state-owned enterprise, state-owned Channel Four Television Corporation. It began its transmission on 2 November 1982 and was established to provide a four ...
have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the
Canadian Aboriginal syllabics Canadian syllabic writing, or simply syllabics, is a family of writing systems used in a number of Indigenous Canadian languages of the Algonquian, Inuit, and (formerly) Athabaskan language families. These languages had no formal writing s ...
letter ᔦ. The
magnetic ink character recognition Magnetic ink character recognition code, known in short as MICR code, is a character recognition technology used mainly by the banking industry to streamline the processing and clearance of cheques and other documents. MICR encoding, called the '' ...
"CMC-7" font also uses this variety of "4".


In religion


Buddhism

*
Four Noble Truths In Buddhism, the Four Noble Truths (Sanskrit: ; pi, cattāri ariyasaccāni; "The four Arya satyas") are "the truths of the Noble Ones", the truths or realities for the "spiritually worthy ones". Four Noble Truths: BUDDHIST PHILOSOPHY Encycl ...
Samudaya In Buddhism, the Four Noble Truths (Sanskrit: ; pi, cattāri ariyasaccāni; "The four Arya satyas") are "the truths of the Noble Ones", the truths or realities for the "spiritually worthy ones".[aFour Noble Truths: BUDDHIST PHILOSOPHY Encycl ...
,
Nirodha In Buddhism, nirodha, "cessation," "extinction," or "suppression," refers to the cessation or renouncing of craving and desire. It is the third of the Four Noble Truths,_stating_that_suffering_(dukkha.html" ;"title="Four Noble Truths: BUDDHIST P ...
, Noble Eightfold Path">Magga The Buddhist path (''marga'') to liberation, also referred to as awakening, is described in a wide variety of ways. The classical one is the Noble Eightfold Path, which is only one of several summaries presented in the Sutta Pitaka. A number of o ...
*Four sights – observations which affected Prince Siddhartha deeply and made him realize the sufferings of all beings, and compelled him to begin his spiritual journey—an old age, old man, a illness, sick man, a death, dead man, and an
ascetic Asceticism (; from the el, ἄσκησις, áskesis, exercise', 'training) is a lifestyle characterized by abstinence from sensual pleasures, often for the purpose of pursuing spiritual goals. Ascetics may withdraw from the world for their p ...
* Four Great Elements
earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
,
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
,
fire Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction Product (chemistry), products. At a certain point in the combustion reaction, called the ignition ...
, and
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hou ...
*
Four Heavenly Kings The Four Heavenly Kings are four Buddhist gods, each of whom is believed to watch over one cardinal direction of the world. In Chinese mythology, they are known collectively as the "Fēng Tiáo Yǔ Shùn" () or "Sìdà Tiānwáng" (). In the a ...
*
Four Foundations of Mindfulness ''Satipatthana'' ( pi, Satipaṭṭhāna, italic=yes; sa, smṛtyupasthāna, italic=yes) is a central practice in the Buddha's teachings, meaning "the establishment of mindfulness" or "presence of mindfulness", or alternatively "foundations of ...
– contemplation of the body, contemplation of feelings, contemplation of mind, contemplation of mental objects *
Four Right Exertions The Four Right Exertions (also known as, Four Proper Exertions, Four Right Efforts, Four Great Efforts, Four Right Endeavors or Four Right Strivings) (Pali: '; Skt.: ' or ') are an integral part of the Buddhist path to Enlightenment (understan ...
* Four Bases of Power * Four jhānas * Four arūpajhānas * Four Divine Abidings
loving-kindness Loving-kindness may refer to: * an English translation of Chesed ( he, חֶסֶד, also Romanized: ) is a Hebrew word that means 'kindness or love between people', specifically of the devotional piety of people towards God as well as of love o ...
,
compassion Compassion motivates people to go out of their way to relieve the physical, mental or emotional pains of others and themselves. Compassion is often regarded as being sensitive to the emotional aspects of the suffering of others. When based on n ...
, sympathetic joy, and
equanimity Equanimity (Latin: ''æquanimitas'', having an even mind; ''aequus'' even; ''animus'' mind/soul) is a state of inner peace, psychological stability and composure which is undisturbed by experience of or exposure to emotions, pain, or other phenom ...
*
Four stages of enlightenment The four stages of awakening in Early Buddhism and Theravada are four progressive stages culminating in full awakening ('' Bodhi'') as an Arahant (SN 22.122). These four stages are Sotāpanna, Sakadāgāmi, Anāgāmi, and Arahant. The oldest B ...
stream-enterer,
once-returner In Buddhism, the Sakadāgāmin (Pali; Sanskrit: ''Sakṛdāgāmin'', ), "returning once"Rhys Davids & Stede (1921-25), p. 660, entry for "Sakadāgāmin" (retrieved 26 Sep 2007 at http://dsal.uchicago.edu/cgi-bin/philologic/getobject.pl?c.3:1:2653. ...
, non-returner, and
arahant In Buddhism, an ''arhat'' (Sanskrit: अर्हत्) or ''arahant'' (Pali: अरहन्त्, 𑀅𑀭𑀳𑀦𑁆𑀢𑁆) is one who has gained insight into the true nature of existence and has achieved ''Nirvana'' and liberated ...
* Four main pilgrimage sites
Lumbini Lumbinī ( ne, लुम्बिनी, IPA=ˈlumbini , "the lovely") is a Buddhist pilgrimage site in the Rupandehi District of Lumbini Province in Nepal. It is the place where, according to Buddhist tradition, Queen Mahamayadevi gave birth ...
,
Bodh Gaya Bodh Gaya is a religious site and place of pilgrimage associated with the Mahabodhi Temple Complex in Gaya district in the Indian state of Bihar. It is famous as it is the place where Gautama Buddha is said to have attained Enlightenment ( pi, ...
,
Sarnath Sarnath (Hindustani pronunciation: aːɾnaːtʰ also referred to as Sarangnath, Isipatana, Rishipattana, Migadaya, or Mrigadava) is a place located northeast of Varanasi, near the confluence of the Ganges and the Varuna rivers in Uttar Pr ...
, and
Kusinara Kushinagar ( Hindustani: or ; Pali: ; Sanskrit: ) is a town in the Kushinagar district in Uttar Pradesh, India. It is an important and popular Buddhist pilgrimage site, where Buddhists believe Gautama Buddha attained ''parinirvana''. Etymo ...


Judeo-Christian symbolism

*The
Tetragrammaton The Tetragrammaton (; ), or Tetragram, is the four-letter Hebrew language, Hebrew theonym (transliterated as YHWH), the name of God in the Hebrew Bible. The four letters, written and read from right to left (in Hebrew), are ''yodh'', ''he (l ...
is the four-letter name of
God In monotheism, monotheistic thought, God is usually viewed as the supreme being, creator deity, creator, and principal object of Faith#Religious views, faith.Richard Swinburne, Swinburne, R.G. "God" in Ted Honderich, Honderich, Ted. (ed)''The Ox ...
. *
Ezekiel Ezekiel (; he, יְחֶזְקֵאל ''Yəḥezqēʾl'' ; in the Septuagint written in grc-koi, Ἰεζεκιήλ ) is the central protagonist of the Book of Ezekiel in the Hebrew Bible. In Judaism, Christianity, and Islam, Ezekiel is acknow ...
has a vision of four
living creatures In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fungi; ...
: a man, a lion, an ox, and an eagle. *The four Matriarchs (foremothers) of
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
are
Sarah Sarah (born Sarai) is a biblical matriarch and prophetess, a major figure in Abrahamic religions. While different Abrahamic faiths portray her differently, Judaism, Christianity, and Islam all depict her character similarly, as that of a piou ...
,
Rebekah Rebecca, ; Syriac: , ) from the Hebrew (lit., 'connection'), from Semitic root , 'to tie, couple or join', 'to secure', or 'to snare') () appears in the Hebrew Bible as the wife of Isaac and the mother of Jacob and Esau. According to biblical ...
,
Leah Leah ''La'ya;'' from (; ) appears in the Hebrew Bible as one of the two wives of the Biblical patriarch Jacob. Leah was Jacob's first wife, and the older sister of his second (and favored) wife Rachel. She is the mother of Jacob's first son ...
, and
Rachel Rachel () was a Biblical figure, the favorite of Jacob's two wives, and the mother of Joseph and Benjamin, two of the twelve progenitors of the tribes of Israel. Rachel's father was Laban. Her older sister was Leah, Jacob's first wife. Her aun ...
. *The Four Species (
lulav ''Lulav'' (; he, לולב) is a closed frond of the date palm tree. It is one of the Four Species used during the Jewish holiday of Sukkot. The other Species are the ''hadass'' (Myrtus, myrtle), '' aravah'' (willow), and ''etrog'' (citron). Wh ...
,
hadass Hadass (Hebrew: הדס, pl. ''hadassim'' - הדסים) is a branch of the myrtle tree that forms part of the lulav used on the Jewish holiday of Sukkot. Hadass is one of the Four species (''arba'ah minim''–ארבעת המינים). T ...
, aravah and
etrog Etrog ( he, אֶתְרוֹג, plural: '; Ashkenazi Hebrew: ', plural: ') is the yellow citron or ''Citrus medica'' used by Jews during the week-long holiday of Sukkot as one of the four species. Together with the ''lulav'', ''hadass'', and '' ...
) are taken as one of the
mitzvot In its primary meaning, the Hebrew word (; he, מִצְוָה, ''mīṣvā'' , plural ''mīṣvōt'' ; "commandment") refers to a commandment commanded by God to be performed as a religious duty. Jewish law () in large part consists of discus ...
on the
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
holiday of
Sukkot or ("Booths, Tabernacles") , observedby = Jews, Samaritans, a few Protestant denominations, Messianic Jews, Semitic Neopagans , type = Jewish, Samaritan , begins = 15th day of Tishrei , ends = 21st day of Tishre ...
. (
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
) *The Four Cups of Wine to drink on the
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
holiday of
Passover Passover, also called Pesach (; ), is a major Jewish holidays, Jewish holiday that celebrates the The Exodus, Biblical story of the Israelites escape from slavery in Ancient Egypt, Egypt, which occurs on the 15th day of the Hebrew calendar, He ...
. (
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
) *The Four Questions to be asked on the
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
holiday of
Passover Passover, also called Pesach (; ), is a major Jewish holidays, Jewish holiday that celebrates the The Exodus, Biblical story of the Israelites escape from slavery in Ancient Egypt, Egypt, which occurs on the 15th day of the Hebrew calendar, He ...
. (
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
) *The Four Sons to be dealt with on the
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
holiday of
Passover Passover, also called Pesach (; ), is a major Jewish holidays, Jewish holiday that celebrates the The Exodus, Biblical story of the Israelites escape from slavery in Ancient Egypt, Egypt, which occurs on the 15th day of the Hebrew calendar, He ...
. (
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
) *The Four Expressions of Redemption to be said on the
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
holiday of
Passover Passover, also called Pesach (; ), is a major Jewish holidays, Jewish holiday that celebrates the The Exodus, Biblical story of the Israelites escape from slavery in Ancient Egypt, Egypt, which occurs on the 15th day of the Hebrew calendar, He ...
. (
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
) *The four
Gospel Gospel originally meant the Christian message ("the gospel"), but in the 2nd century it came to be used also for the books in which the message was set out. In this sense a gospel can be defined as a loose-knit, episodic narrative of the words an ...
s:
Matthew Matthew may refer to: * Matthew (given name) * Matthew (surname) * ''Matthew'' (ship), the replica of the ship sailed by John Cabot in 1497 * ''Matthew'' (album), a 2000 album by rapper Kool Keith * Matthew (elm cultivar), a cultivar of the Ch ...
,
Mark Mark may refer to: Currency * Bosnia and Herzegovina convertible mark, the currency of Bosnia and Herzegovina * East German mark, the currency of the German Democratic Republic * Estonian mark, the currency of Estonia between 1918 and 1927 * Fi ...
,
Luke People *Luke (given name), a masculine given name (including a list of people and characters with the name) *Luke (surname) (including a list of people and characters with the name) *Luke the Evangelist, author of the Gospel of Luke. Also known as ...
, and
John John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second ...
. (
Christianity Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global pop ...
) *The
Four Horsemen of the Apocalypse The Four Horsemen of the Apocalypse are figures in the Christian scriptures, first appearing in the Book of Revelation, a piece of apocalypse literature written by John of Patmos. Revelation 6 tells of a book or scroll in God's right hand tha ...
ride in the
Book of Revelation The Book of Revelation is the final book of the New Testament (and consequently the final book of the Christian Bible). Its title is derived from the first word of the Koine Greek text: , meaning "unveiling" or "revelation". The Book of R ...
. (
Christianity Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global pop ...
) *The four holy cities of Judaism:
Jerusalem Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...
,
Hebron Hebron ( ar, الخليل or ; he, חֶבְרוֹן ) is a Palestinian. city in the southern West Bank, south of Jerusalem. Nestled in the Judaean Mountains, it lies above sea level. The second-largest city in the West Bank (after East J ...
,
Safed Safed (known in Hebrew language, Hebrew as Tzfat; Sephardi Hebrew, Sephardic Hebrew & Modern Hebrew: צְפַת ''Tsfat'', Ashkenazi Hebrew pronunciation, Ashkenazi Hebrew: ''Tzfas'', Biblical Hebrew: ''Ṣǝp̄aṯ''; ar, صفد, ''Ṣafad''), i ...
, and
Tiberius Tiberius Julius Caesar Augustus (; 16 November 42 BC – 16 March AD 37) was the second Roman emperor. He reigned from AD 14 until 37, succeeding his stepfather, the first Roman emperor Augustus. Tiberius was born in Rome in 42 BC. His father ...


Hinduism

*There are four
Vedas upright=1.2, The Vedas are ancient Sanskrit texts of Hinduism. Above: A page from the '' Atharvaveda''. The Vedas (, , ) are a large body of religious texts originating in ancient India. Composed in Vedic Sanskrit, the texts constitute the ...
: Rigveda, Samaveda, Yajurveda and Atharvaveda. *In
Puruṣārtha ''Purushartha'' (Sanskrit: पुरुषार्थ, International Alphabet of Sanskrit Transliteration, IAST: ) literally means "object(ive) of men".Dharma Dharma (; sa, धर्म, dharma, ; pi, dhamma, italic=yes) is a key concept with multiple meanings in Indian religions, such as Hinduism, Buddhism, Jainism, Sikhism and others. Although there is no direct single-word translation for '' ...
,
Artha ''Artha'' (; sa, अर्थ; Tamil: ''poruḷ'' / ''பொருள்'') is one of the four aims of human life in Indian philosophy.James Lochtefeld (2002), The Illustrated Encyclopedia of Hinduism, Rosen Publishing, New York, , pp 55–56 T ...
,
Kāma ''Kama'' (Sanskrit ) means "desire, wish, longing" in Hindu texts, Hindu, Buddhist texts, Buddhist, Jain literature, Jain, and Sikh literature, Sikh literature.Monier Williamsकाम, kāmaMonier-Williams Sanskrit English Dictionary, pp 27 ...
,
Moksha ''Moksha'' (; sa, मोक्ष, '), also called ''vimoksha'', ''vimukti'' and ''mukti'', is a term in Hinduism, Buddhism, Jainism and Sikhism for various forms of emancipation, enlightenment, liberation, and release. In its soteriology, ...
. *The four stages of life
Brahmacharya ''Brahmacharya'' (; sa, ब्रह्मचर्य ) is a concept within Indian religions that literally means to stay in conduct within one's own Self. In Yoga, Hinduism, Buddhism and Jainism it generally refers to a lifestyle charac ...
(student life), Grihastha (household life), Vanaprastha (retired life) and
Sannyasa ''Sannyasa'' (Sanskrit: संन्यास; IAST: ), sometimes spelled Sanyasa (सन्न्यास) or Sanyasi (for the person), is life of renunciation and the fourth stage within the Hindu system of four life stages known as '' As ...
(renunciation). *The four primary castes or strata of society:
Brahmana The Brahmanas (; Sanskrit: , ''Brāhmaṇam'') are Vedic śruti works attached to the Samhitas (hymns and mantras) of the Rig, Sama, Yajur, and Atharva Vedas. They are a secondary layer or classification of Sanskrit texts embedded within ea ...
(priest/teacher),
Kshatriya Kshatriya ( hi, क्षत्रिय) (from Sanskrit ''kṣatra'', "rule, authority") is one of the four varna (social orders) of Hindu society, associated with warrior aristocracy. The Sanskrit term ''kṣatriyaḥ'' is used in the con ...
(warrior/politician),
Vaishya Vaishya (Sanskrit: वैश्य, ''vaiśya'') is one of the four Varna (Hinduism), varnas of the Hinduism, Hindu social order in India. Vaishyas are classed third in the order of caste hierarchy. The occupation of Vaishyas consists mainly ...
(landowner/entrepreneur) and
Shudra Shudra or ''Shoodra'' (Sanskrit: ') is one of the four '' varnas'' of the Hindu caste system and social order in ancient India. Various sources translate it into English as a caste, or alternatively as a social class. Theoretically, class ser ...
(servant/manual laborer). *The
swastika The swastika (卐 or 卍) is an ancient religious and cultural symbol, predominantly in various Eurasian, as well as some African and American cultures, now also widely recognized for its appropriation by the Nazi Party and by neo-Nazis. It ...
symbol is traditionally used in
Hindu Hindus (; ) are people who religiously adhere to Hinduism.Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pages 35–37 Historically, the term has also been used as a geographical, cultural, and later religious identifier for ...
religions as a sign of good luck and signifies good from all four directions. *The god
Brahma Brahma ( sa, ब्रह्मा, Brahmā) is a Hindu god, referred to as "the Creator" within the Trimurti, the trinity of supreme divinity that includes Vishnu, and Shiva.Jan Gonda (1969)The Hindu Trinity Anthropos, Bd 63/64, H 1/2, pp. 21 ...
has four faces. *There are four ''
yuga A ''yuga'', in Hinduism, is generally used to indicate an age of time. In the ''Rigveda'', a ''yuga'' refers to generations, a long period, a very brief period, or a yoke (joining of two things). In the ''Mahabharata'', the words ''yuga'' and ...
s'': ''
Satya ''Satya'' (Sanskrit: सत्य; IAST: ''satya)'' is a Sanskrit word loosely translated as truth, essence. A. A. Macdonell, ''Sanskrit English Dictionary'', Asian Educational Services, , pp. 330–331 It also refers to a virtue in Indian relig ...
'', '' Dvapara'', ''
Treta ''Treta Yuga'', in Hinduism, is the second and second best of the four '' yugas'' (world ages) in a ''Yuga Cycle'', preceded by '' Krita (Satya) Yuga'' and followed by '' Dvapara Yuga''. ''Treta Yuga'' lasts for 1,296,000 years (3,600 divine year ...
'' and ''
Kali Kali (; sa, काली, ), also referred to as Mahakali, Bhadrakali, and Kalika ( sa, कालिका), is a Hinduism, Hindu goddess who is considered to be the goddess of ultimate power, time, destruction and change in Shaktism. In t ...
''


Islam

*
Eid al-Adha Eid al-Adha () is the second and the larger of the two main holidays celebrated in Islam (the other being Eid al-Fitr). It honours the willingness of Ibrahim (Abraham) to sacrifice his son Ismail (Ishmael) as an act of obedience to Allah's co ...
lasts for four days, from the 10th to the 14th of
Dhul Hijja Dhu al-Hijja ( ar, ذُو ٱلْحِجَّة, translit=Ḏū al-Ḥijja, ), also spelled Zu al-Hijja, is the twelfth and final month in the Islamic calendar. It is a very sacred month in the Islamic calendar, one in which the '' Ḥajj'' (Pilgri ...
. *The four holy cities of Islam: Mecca, Medina, Jerusalem and Damascus. *The four tombs in the Green Dome: Muhammad, Abu Bakr, Umar ibn Khattab and Isa ibn Maryam (Jesus). *There are four
Rashidun , image = تخطيط كلمة الخلفاء الراشدون.png , caption = Calligraphic representation of Rashidun Caliphs , birth_place = Mecca, Hejaz, Arabia present-day Saudi Arabia , known_for = Companions of t ...
or Rightly Guided
Caliph A caliphate or khilāfah ( ar, خِلَافَة, ) is an institution or public office under the leadership of an Islamic steward with the title of caliph (; ar, خَلِيفَة , ), a person considered a political-religious successor to th ...
s:
Abu Bakr Abu Bakr Abdallah ibn Uthman Abi Quhafa (; – 23 August 634) was the senior companion and was, through his daughter Aisha, a father-in-law of the Islamic prophet Muhammad, as well as the first caliph of Islam. He is known with the honor ...
,
Umar ibn al-Khattab ʿUmar ibn al-Khaṭṭāb ( ar, عمر بن الخطاب, also spelled Omar, ) was the second Rashidun caliph, ruling from August 634 until his assassination in 644. He succeeded Abu Bakr () as the second caliph of the Rashidun Caliphate o ...
,
Uthman ibn Affan Uthman ibn Affan ( ar, عثمان بن عفان, ʿUthmān ibn ʿAffān; – 17 June 656), also spelled by Colloquial Arabic, Turkish and Persian rendering Osman, was a second cousin, son-in-law and notable companion of the Islamic proph ...
and
Ali ibn Abi Talib ʿAlī ibn Abī Ṭālib ( ar, عَلِيّ بْن أَبِي طَالِب; 600 – 661 CE) was the last of four Rightly Guided Caliphs to rule Islam (r. 656 – 661) immediately after the death of Muhammad, and he was the first Shia Imam. ...
. *The Four Arch Angels in Islam are: Jibraeel (Gabriel), Mikaeel (Michael), Izraeel (Azrael), and Israfil (Raphael) *There are four months in which war is not permitted:
Muharram Muḥarram ( ar, ٱلْمُحَرَّم) (fully known as Muharram ul Haram) is the first month of the Islamic calendar. It is one of the four sacred months of the year when warfare is forbidden. It is held to be the second holiest month after R ...
,
Rajab Rajab ( ar, رَجَب) is the seventh month of the Islamic calendar. The lexical definition of the classical Arabic verb ''rajaba'' is "to respect" which could also mean "be awe or be in fear", of which Rajab is a derivative. This month is re ...
,
Dhu al-Qi'dah Dhu al-Qa'dah ( ar, ذُو ٱلْقَعْدَة, ', ), also spelled Dhu al-Qi'dah or Zu al-Qa'dah, is the eleventh month in the Islamic calendar. It could possibly mean "possessor or owner of the sitting and seating place" - the space occupied w ...
and
Dhu al-Hijjah Dhu al-Hijja ( ar, ذُو ٱلْحِجَّة, translit=Ḏū al-Ḥijja, ), also spelled Zu al-Hijja, is the twelfth and final month in the Islamic calendar. It is a very sacred month in the Islamic calendar, one in which the ''Hajj, Ḥajj'' (P ...
. *There are four
Sunni Sunni Islam () is the largest branch of Islam, followed by 85–90% of the world's Muslims. Its name comes from the word '' Sunnah'', referring to the tradition of Muhammad. The differences between Sunni and Shia Muslims arose from a disagr ...
schools of
fiqh ''Fiqh'' (; ar, فقه ) is Islamic jurisprudence. Muhammad-> Companions-> Followers-> Fiqh. The commands and prohibitions chosen by God were revealed through the agency of the Prophet in both the Quran and the Sunnah (words, deeds, and ...
:
Hanafi The Hanafi school ( ar, حَنَفِية, translit=Ḥanafiyah; also called Hanafite in English), Hanafism, or the Hanafi fiqh, is the oldest and one of the four traditional major Sunni schools ( maddhab) of Islamic Law (Fiqh). It is named aft ...
,
Shafi`i The Shafii ( ar, شَافِعِي, translit=Shāfiʿī, also spelled Shafei) school, also known as Madhhab al-Shāfiʿī, is one of the four major traditional schools of religious law (madhhab) in the Sunnī branch of Islam. It was founded by ...
,
Maliki The ( ar, مَالِكِي) school is one of the four major schools of Islamic jurisprudence within Sunni Islam. It was founded by Malik ibn Anas in the 8th century. The Maliki school of jurisprudence relies on the Quran and hadiths as primary ...
and
Hanbali The Hanbali school ( ar, ٱلْمَذْهَب ٱلْحَنۢبَلِي, al-maḏhab al-ḥanbalī) is one of the four major traditional Sunni schools (''madhahib'') of Islamic jurisprudence. It is named after the Arab scholar Ahmad ibn Hanbal ...
. *There are four major Sunni Imams:
Abū Ḥanīfa Nuʿmān ibn Thābit ibn Zūṭā ibn Marzubān ( ar, نعمان بن ثابت بن زوطا بن مرزبان; –767), commonly known by his '' kunya'' Abū Ḥanīfa ( ar, أبو حنيفة), or reverently as Imam Abū Ḥanīfa by Sunni Musl ...
,
Muhammad ibn Idris ash-Shafi`i Abū ʿAbdillāh Muḥammad ibn Idrīs al-Shāfiʿī ( ar, أَبُو عَبْدِ ٱللهِ مُحَمَّدُ بْنُ إِدْرِيسَ ٱلشَّافِعِيُّ, 767–19 January 820 CE) was an Arab Muslim theologian, writer, and schola ...
,
Malik ibn Anas Malik ibn Anas ( ar, مَالِك بن أَنَس, ‎ 711–795 CE / 93–179 AH), whose full name is Mālik bin Anas bin Mālik bin Abī ʿĀmir bin ʿAmr bin Al-Ḥārith bin Ghaymān bin Khuthayn bin ʿAmr bin Al-Ḥārith al-Aṣbaḥī ...
and
Ahmad ibn Hanbal Ahmad ibn Hanbal al-Dhuhli ( ar, أَحْمَد بْن حَنْبَل الذهلي, translit=Aḥmad ibn Ḥanbal al-Dhuhlī; November 780 – 2 August 855 CE/164–241 AH), was a Muslim jurist, theologian, ascetic, hadith traditionist, and ...
. *There are four books in Islam: Taurait, Zaboor, Injeel, Quran. *Waiting for four months is ordained for those who take an oath for abstention from their wives. *The waiting period of the woman whose husband dies is four months and ten days. *When Abraham said: "My Lord, show me how You give life to the dead," Allah said: "Why! Do you have no faith?" Abraham replied: "Yes, but in order that my heart be at rest." He said: "Then take four birds, and tame them to yourself, then put a part of them on every hill, and summon them; they will come to you flying. l-Baqara 2:260*The respite of four months was granted to give time to the mushriks in Surah
At-Tawba At-Tawbah ( ar, ٱلتوبة, ; The Repentance), also known as Bara'ah ( ar, براءة, ; Repudiation), is the ninth chapter (''sūrah'') of the Quran. It contains 129 verses ('' āyāt'') and is one of the last Medinan surahs. This Surah is ...
so that they should consider their position carefully and decide whether to make preparation for war or to emigrate from the country or to accept Islam. *Those who accuse honorable women (of unchastity) but do not produce four witnesses, flog them with eighty lashes, and do not admit their testimony ever after. They are indeed transgressors. n-Noor 24:4


Taoism

*
Four Symbols The Four Symbols (, literally meaning "four images"), are four mythological creatures appearing among the Chinese constellations along the ecliptic, and viewed as the guardians of the four cardinal directions. These four creatures are also refe ...
of
I Ching The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Zho ...


Other

*In a more general sense, numerous mythological and cosmogonical systems consider
Four corners of the world Several cosmological and mythological systems portray four corners of the world or four quarters of the world corresponding approximately to the four points of the compass (or the two solstices and two equinoxes). At the center may lie a sacred ...
as essentially corresponding to the four points of the compass. *Four is the sacred number of the
Zia Zia or ZIA (also spelled Ziya, Ḍiya , Dia or Diya) may refer to: People * Zia (name), including a list of people and fictional characters with the name ** A romanization of the Wu ( Shanghainese) pronunciation of the Chinese surname Xie (謝) ...
, an indigenous tribe located in the U.S. state of
New Mexico ) , population_demonym = New Mexican ( es, Neomexicano, Neomejicano, Nuevo Mexicano) , seat = Santa Fe , LargestCity = Albuquerque , LargestMetro = Tiguex , OfficialLang = None , Languages = English, Spanish ( New Mexican), Navajo, Ker ...
. *The Chinese, the Koreans, and the Japanese are superstitious about the number four because it is a
homonym In linguistics, homonyms are words which are homographs (words that share the same spelling, regardless of pronunciation), or homophones (equivocal words, that share the same pronunciation, regardless of spelling), or both. Using this definition, ...
for "death" in their languages. *In
Slavic mythology Slavic mythology or Slavic religion is the religious beliefs, myths, and ritual practices of the Slavs before Christianisation, which occurred at various stages between the 8th and the 13th century. The South Slavs, who likely settled in the B ...
, the god
Svetovid Svetovit, Sventovit, Svantovit is the god of abundance and war, and the chief god of the Slavic tribe of the Rani, and later of all the Polabian Slavs. His organized cult was located on the island of Rügen, at Cape Arkona, where his main temp ...
has four heads.


In politics

*
Four Freedoms The Four Freedoms were goals articulated by U.S. President Franklin D. Roosevelt on Monday, January 6, 1941. In an address known as the Four Freedoms speech (technically the 1941 State of the Union address), he proposed four fundamental freed ...
: four fundamental freedoms that
Franklin D. Roosevelt Franklin Delano Roosevelt (; ; January 30, 1882April 12, 1945), often referred to by his initials FDR, was an American politician and attorney who served as the 32nd president of the United States from 1933 until his death in 1945. As the ...
declared ought to be enjoyed by everyone in the world: Freedom of Speech, Freedom of Religion, Freedom from Want, Freedom from Fear. *
Gang of Four The Gang of Four () was a Maoist political faction composed of four Chinese Communist Party (CCP) officials. They came to prominence during the Cultural Revolution (1966–1976) and were later charged with a series of treasonous crimes. The gang ...
: Popular name for four Chinese Communist Party leaders who rose to prominence during China's Cultural Revolution, but were ousted in 1976 following the death of Chairman
Mao Zedong Mao Zedong pronounced ; also romanised traditionally as Mao Tse-tung. (26 December 1893 – 9 September 1976), also known as Chairman Mao, was a Chinese communist revolutionary who was the founder of the People's Republic of China (PRC) ...
. Among the four was Mao's widow,
Jiang Qing Jiang Qing (19 March 191414 May 1991), also known as Madame Mao, was a Chinese communist revolutionary, actress, and major political figure during the Cultural Revolution (1966–1976). She was the fourth wife of Mao Zedong, the Chairman o ...
. Since then, many other political factions headed by four people have been called "Gangs of Four".


In computing

*Four
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 (half 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 ...
) are sometimes called a
nibble In computing, a nibble (occasionally nybble, nyble, or nybl to match the spelling of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte or tetrade. In a networking or telecommunication context, the nibble is oft ...
.


In science

*A
tetramer A tetramer () (''tetra-'', "four" + '' -mer'', "parts") is an oligomer formed from four monomers or subunits. The associated property is called ''tetramery''. An example from inorganic chemistry is titanium methoxide with the empirical formula Ti ...
is an
oligomer In chemistry and biochemistry, an oligomer () is a molecule that consists of a few repeating units which could be derived, actually or conceptually, from smaller molecules, monomers.Quote: ''Oligomer molecule: A molecule of intermediate relativ ...
formed out of four sub-units.


In astronomy

*Four terrestrial (or rocky) planets in the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
:
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
,
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...
,
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
, and
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...
. *Four giant gas/ice planets in the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
:
Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
,
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
,
Uranus Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus (mythology), Uranus (Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars (mythology), Mars), grandfather ...
, and
Neptune Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times ...
. *Four of Jupiter's moons (the
Galilean moons The Galilean moons (), or Galilean satellites, are the four largest moons of Jupiter: Io, Europa, Ganymede, and Callisto. They were first seen by Galileo Galilei in December 1609 or January 1610, and recognized by him as satellites of Jupiter ...
) are readily visible from Earth with a hobby telescope. *
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 ...
M4, a magnitude 7.5
globular cluster A globular cluster is a spheroidal conglomeration of stars. Globular clusters are bound together by gravity, with a higher concentration of stars towards their centers. They can contain anywhere from tens of thousands to many millions of membe ...
in the constellation
Scorpius Scorpius is a zodiac constellation located in the Southern celestial hemisphere, where it sits near the center of the Milky Way, between Libra to the west and Sagittarius to the east. Scorpius is an ancient constellation that pre-dates the Gre ...
. *The Roman numeral IV stands for
subgiant A subgiant is a star that is brighter than a normal main-sequence star of the same spectral class, but not as bright as giant stars. The term subgiant is applied both to a particular spectral luminosity class and to a stage in the evolution of ...
in the
Yerkes spectral classification scheme In astronomy, stellar classification is the classification of stars based on their stellar spectrum, spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a Prism (optics), prism or diffraction grati ...
.


In biology

*Four is the number of
nucleobase Nucleobases, also known as ''nitrogenous bases'' or often simply ''bases'', are nitrogen-containing biological compounds that form nucleosides, which, in turn, are components of nucleotides, with all of these monomers constituting the basic b ...
types in DNA and
RNA Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
adenine Adenine () ( symbol A or Ade) is a nucleobase (a purine derivative). It is one of the four nucleobases in the nucleic acid of DNA that are represented by the letters G–C–A–T. The three others are guanine, cytosine and thymine. Its derivati ...
,
guanine Guanine () ( symbol G or Gua) is one of the four main nucleobases found in the nucleic acids DNA and RNA, the others being adenine, cytosine, and thymine (uracil in RNA). In DNA, guanine is paired with cytosine. The guanine nucleoside is called ...
,
cytosine Cytosine () ( symbol C or Cyt) is one of the four nucleobases found in DNA and RNA, along with adenine, guanine, and thymine (uracil in RNA). It is a pyrimidine derivative, with a heterocyclic aromatic ring and two substituents attached (an am ...
,
thymine Thymine () ( symbol T or Thy) is one of the four nucleobases in the nucleic acid of DNA that are represented by the letters G–C–A–T. The others are adenine, guanine, and cytosine. Thymine is also known as 5-methyluracil, a pyrimidine nu ...
(
uracil Uracil () (symbol U or Ura) is one of the four nucleobases in the nucleic acid RNA. The others are adenine (A), cytosine (C), and guanine (G). In RNA, uracil binds to adenine via two hydrogen bonds. In DNA, the uracil nucleobase is replaced by ...
in
RNA Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
). *Many
chordate A chordate () is an animal of the phylum Chordata (). All chordates possess, at some point during their larval or adult stages, five synapomorphies, or primary physical characteristics, that distinguish them from all the other taxa. These fiv ...
s have four feet, legs or leglike appendages (
tetrapods Tetrapods (; ) are four-limbed vertebrate animals constituting the superclass Tetrapoda (). It includes extant and extinct amphibians, sauropsids (reptiles, including dinosaurs and therefore birds) and synapsids (pelycosaurs, extinct therapsids ...
). *The
mammal Mammals () are a group of vertebrate animals constituting the class Mammalia (), characterized by the presence of mammary glands which in females produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or ...
ian
heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide t ...
consists of four chambers. *Many
mammal Mammals () are a group of vertebrate animals constituting the class Mammalia (), characterized by the presence of mammary glands which in females produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or ...
s (
Carnivora Carnivora is a Clade, monophyletic order of Placentalia, placental mammals consisting of the most recent common ancestor of all felidae, cat-like and canidae, dog-like animals, and all descendants of that ancestor. Members of this group are f ...
,
Ungulata Ungulates ( ) are members of the diverse clade Ungulata which primarily consists of large mammals with hooves. These include odd-toed ungulates such as horses, rhinoceroses, and tapirs; and even-toed ungulates such as cattle, pigs, giraffes, ...
) use four fingers for movement. *All
insect Insects (from Latin ') are pancrustacean hexapod invertebrates of the class Insecta. They are the largest group within the arthropod phylum. Insects have a chitinous exoskeleton, a three-part body ( head, thorax and abdomen), three pairs ...
s with wings except
flies Flies are insects of the order Diptera, the name being derived from the Greek δι- ''di-'' "two", and πτερόν ''pteron'' "wing". Insects of this order use only a single pair of wings to fly, the hindwings having evolved into advanced ...
and some others have four
wing A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is expres ...
s. *Insects of the superorder
Endopterygota Endopterygota (from Ancient Greek ''endon'' 'inner' + ''pterón'' 'wing' + New Latin ''-ota'' 'having'), also known as Holometabola, is a superorder of insects within the infraclass Neoptera that go through distinctive larval, pupal, and adult s ...
, also known as Holometabola, such as butterflies, ants, bees, beetles, fleas, flies, moths, and wasps, undergo
holometabolism Holometabolism, also called complete metamorphosis, is a form of insect development which includes four life stages: egg, larva, pupa, and imago (or adult). Holometabolism is a synapomorphic trait of all insects in the superorder Endopterygot ...
—complete metamorphism in four stages—from (1) embryo (ovum, egg), to (2) larva (such as grub, caterpillar), then (3) pupa (such as the chrysalis), and finally (4) the imago. *In the common
ABO blood group system The ABO blood group system is used to denote the presence of one, both, or neither of the A and B antigens on erythrocytes. For human blood transfusions, it is the most important of the 43 different blood type (or group) classification system ...
, there are four blood types (A, B, O, AB). *
Humans Humans (''Homo sapiens'') are the most abundant and widespread species of primate, characterized by bipedalism and exceptional cognitive skills due to a large and complex brain. This has enabled the development of advanced tools, culture, ...
have four canine tooth, canines and four wisdom teeth. *The cow's stomach is divided in four digestive compartments: reticulum, rumen, omasum and abomasum.


In chemistry

*Valence (chemistry), Valency of carbon (that is basis of life on the Earth) is four. Also because of its tetrahedral crystal bond structure, diamond (one of the natural allotropes of carbon) is the hardest known naturally occurring material. It is also the valence of silicon, whose compounds form the majority of the mass of the Earth's crust. *The atomic number of beryllium *There are four basic states of matter: solid, liquid, gas, and plasma (physics), plasma.


In physics

*Special relativity and general relativity treat nature as four-
dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
al: Three-dimensional space (mathematics), 3D regular space and one-dimensional time are treated together and called spacetime. Also, any event ''E'' has a light cone composed of four zones of possible communication and cause and effect (outside the light cone is strictly incommunicado). *There are four fundamental forces (electromagnetism, gravitation, the weak nuclear force, and the strong nuclear force). *In statistical mechanics, the four functions inequality is an inequality for four functions on a finite distributive lattice.


In logic and philosophy

*The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth", which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects' doings. *The Square of Opposition, in both its Aristotelian version and its Square of Opposition#Modern squares of opposition, Boolean version, consists of four forms: A ("All ''S'' is ''R''"), I ("Some ''S'' is ''R''"), E ("No ''S'' is ''R''"), and O ("Some ''S'' is not ''R''"). *In regard to whether two given propositions can have the same truth value, there are four separate logical possibilities: the propositions are ''subalterns'' (possibly both are true, and possibly both are false); ''subcontraries'' (both may be true, but not that both are false); ''contraries'' (both may be false, but not that both are true); or ''contradictories'' (it is not possible that both are true, and it is not possible that both are false). *Aristotle held that there are basically four causes in nature: the Four causes#Material cause, material, the Four causes#Formal cause, formal, the Four causes#Efficient cause, efficient, and the Four causes#Final cause, final. *The Stoicism, Stoics held with four basic categories (Stoic), categories, all viewed as bodies (substantial and insubstantial): (1) ''substance'' in the sense of substrate, primary formless matter; (2) ''quality'', matter's organization to differentiate and individualize something, and coming down to a physical ingredient such as ''pneuma'', breath; (3) ''somehow holding'' (or ''disposed''), as in a posture, state, shape, size, action, and (4) ''somehow holding'' (or ''disposed'') ''toward something,'' as in relative location, familial relation, and so forth. *Immanuel Kant expounded a Category (Kant)#The table of judgments, table of judgments involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a Category (Kant)#The table of categories, table of four categories, named by the terms just listed, and each with three subcategories. *Arthur Schopenhauer's doctoral thesis was ''On the Fourfold Root of the Principle of Sufficient Reason''. *Franz Brentano held that any major philosophical period has four phases: (1) Creative and rapidly progressing with scientific interest and results; then declining through the remaining phases, (2) practical, (3) increasingly skeptical, and (4) literary, mystical, and scientifically worthless—until philosophy is renewed through a new period's first phase. (See Brentano's essay "The Four Phases of Philosophy and Its Current State" 1895, tr. by Mezei and Smith 1998.) *Charles Sanders Peirce, C. S. Peirce, usually a trichotomy (philosophy), trichotomist, discussed four methods for overcoming troublesome uncertainties and achieving secure beliefs: (1) the method of tenacity (policy of sticking to initial belief), (2) the method of authority, (3) the method of congruity (following a fashionable paradigm), and (4) the Fallibilism, fallibilistic, self-correcting method of science (see "s:The Fixation of Belief, The Fixation of Belief", 1877); and four barriers to inquiry, barriers refused by the fallibilist: (1) assertion of absolute certainty; (2) maintaining that something is unknowable; (3) maintaining that something is inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (see
F.R.L.
[First Rule of Logic], 1899). *Paul Weiss (philosopher), Paul Weiss built a system involving four modes of being: Actualities (substances in the sense of substantial, spatiotemporally finite beings), Ideality or Possibility (pure normative form), Existence (the dynamic field), and God (unity). (See Weiss's ''Modes of Being'', 1958). *Karl Popper outlined a tetradic schema to describe the growth of theories and, via generalization, also the emergence of new behaviors and living organisms: (1) problem, (2) tentative theory, (3) (attempted) error-elimination (especially by way of critical discussion), and (4) new problem(s). (See Popper's ''Objective Knowledge'', 1972, revised 1979.) *John Boyd (military strategist) made his key concept the decision cycle or John Boyd (military strategist)#OODA loop, OODA loop, consisting of four stages: (1) observation (data intake through the senses), (2) orientation (analysis and synthesis of data), (3) decision, and (4) action. Boyd held that his decision cycle has philosophical generality, though for strategists the point remains that, through swift decisions, one can disrupt an opponent's decision cycle. *Richard McKeon outlined four classes (each with four subclasses) of modes of philosophical inquiry: (1) Modes of Being (Being); (2) Modes of Thought (That which is); (3) Modes of Fact (Existence); (4) Modes of Simplicity (Experience)—and, corresponding to them, four classes (each with four subclasses) of philosophical semantics: Principles, Methods, Interpretations, and Selections. (See McKeon's "Philosophic Semantics and Philosophic Inquiry" in ''Freedom and History and Other Essays'', 1989.) *Jonathan Lowe (E.J. Lowe) argues in ''The Four-Category Ontology'', 2006, for four categories: ''kinds'' (substantial universals), ''attributes'' (relational universals and property-universals), ''objects'' (substantial particulars), and ''modes'' (relational particulars and property-particulars, also known as "trope (philosophy), tropes"). (See Lowe's "Recent Advances in Metaphysics," 2001
Eprint
*Four opposed camps of the morality and nature of evil: moral absolutism, amoralism, moral relativism, and moral universalism.


In technology

*The resin identification code used in recycling to identify low-density polyethylene. *Most furniture has four legs – tables, chairs, etc. *The four color process (CMYK) is used for printing. *Wide use of
rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containi ...
s (with four angles and four sides) because they have effective form and capability for close adjacency to each other (houses, rooms, tables, bricks, sheets of paper, screens, film frames). *In the Rich Text Format specification, language code 4 is for the Chinese language. Codes for regional variants of Chinese are congruent to . *Credit card machines have four-twelve function keys. *On most phones, the 4 key is associated with the letters G, H, and I, but on the BlackBerry Pearl, it is the key for D and F. *On many computer keyboards, the "4" key may also be used to type the dollar sign ($) if the shift key is held down. *It is the number of
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 a
nibble In computing, a nibble (occasionally nybble, nyble, or nybl to match the spelling of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte or tetrade. In a networking or telecommunication context, the nibble is oft ...
, equivalent to half 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 ...
*In internet slang, "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you". *In Leetspeak, "4" may be used to replace the letter "A". *The Internet protocol suite, TCP/IP stack consists of four layers.


In transport

*Many internal combustion engines are called four-stroke engines because they complete one thermodynamic cycle in four distinct steps: Intake, compression, power, and exhaust. *Most vehicles, including motor vehicles, and particularly automobile, cars/automobiles and light commercial vehicles have four road wheels. *"quattro (four wheel drive system), Quattro", meaning four in the Italian language, is used by Audi as a trademark to indicate that all-wheel drive (AWD) technologies are used on Audi-branded cars. The word "Quattro" was initially used by Audi in 1980 in its original 4WD coupé, the Audi Quattro. Audi also has a privately held subsidiary company called quattro GmbH. *List of highways numbered 4


In sports

* In the Australian Football League, the top level of Australian rules football, each team is allowed 4 "Interchange (Australian rules football), interchanges" (substitute players), who can be freely substituted at any time, subject to a limit on the total number of substitutions. *In baseball: **There are four bases in the game: first base, second base, third base, and home plate; to score a run, an offensive player must complete, in the sequence shown, a circuit of those four bases. ** When a batter receives four pitches that the umpire declares to be "Strike zone, balls" in a single at-bat, a base on balls, informally known as a "walk", is awarded, with the batter sent to first base. **For scoring, number 4 is assigned to the second baseman. **Four is the most runs that can be scored on any single at bat, whereby all three baserunners and the batter score (the most common being via a grand slam (baseball), grand slam). **The fourth batter in the batting lineup is called the cleanup hitter. *In basketball, the number four is used to designate the Power forward (basketball), power forward position, often referred to as "the four spot" or "the four". *In cricket, a four is a specific type of scoring event, whereby the ball crosses the boundary (cricket), boundary after touching the ground at least one time, scoring four runs. Taking four wickets in four consecutive balls is typically referred to as a double hat trick (two consecutive, overlapping hat tricks). *In American Football teams get four downs to reach the line of gain. *In rowing (sport), rowing, a four refers to a boat for four rowers, with or without coxswain. In rowing nomenclature, 4− represents a coxless four and 4+ represents a coxed four. *In rugby league: ** A Try (rugby), try is worth 4 points. ** One of the two starting centres wears the jersey number 4. (An exception to this rule is the Super League, which uses static squad numbering.) *In rugby union: ** One of the two starting Lock (rugby union), locks wears the jersey number 4. ** In the standard Rugby union bonus points system, bonus points system, a point is awarded in the league standings to a team that scores at least 4 tries in a match, regardless of the match result.


In other fields

* The phrase "four-letter word" is used to describe many profanity, swear words in the English language. *Four is the only number whose name in English has the same number of letters as its value. *Four (, formal writing: , pinyin sì) is considered an unlucky number in Chinese culture, Chinese, Korean culture, Korean, Culture of Vietnam, Vietnamese and Culture of Japan, Japanese cultures mostly in Eastern Asia because it sounds like the word "death" (, pinyin sǐ). To avoid complaints from people with tetraphobia, many numbered product lines skip the "four": e.g. Nokia cell phones (there was no series beginning with a 4 until the Nokia 4.2), PalmOne, Inc., Palm Personal digital assistant, PDAs, etc. Some buildings skip floor 4 or replace the number with the letter "F", particularly in heavily Asian areas. ''See tetraphobia'' and ''Numbers in Chinese culture''. *In Pythagorean numerology (a pseudocience) the number 4 represents security and stability. *The number of characters in a canonical four-character idiom (disambiguation), four-character idiom. *In the ICAO spelling alphabet, NATO phonetic alphabet, the digit 4 is called "fower". *In astrology, Cancer (constellation), Cancer is the 4th astrological sign of the Zodiac. *In Tarot, The Emperor (Tarot card), The Emperor is the fourth trump (card games), trump or Major Arcana card. *In ''Tetris'', a game named for the Greek word for 4, every shape in the game is formed of 4 blocks each. *4 represents the number of Justices on the Supreme Court of the United States necessary to grant a writ of certiorari (i.e., agree to hear a case; it is one less than the number necessary to render a majority decision) at the court's current size. *Number Four is a character in the book series ''Lorien Legacies.'' *In the performing arts, the fourth wall is an imaginary barrier which separates the audience from the performers, and is "broken" when performers communicate directly to the audience.


In music

*In written music, Time signature, common time is constructed of four beats per measure and a quarter note receives one beat. *In popular or Popular music, modern music, the most common time signature is also founded on four beats, i.e., 4/4 having four quarter note beats. *The common major scale is built on two sets of four notes (e.g., CDEF, GABC), where the first and last notes create an octave interval (a pair-of-four relationship). *The interval of a perfect fourth is a foundational element of many genres of music, represented in music theory as the tonic (music), tonic and subdominant relationship. Four is also embodied within the circle of fifths (also known as circle of fourths), which reveals the interval of four in more active harmonic contexts. *The typical number of movements in a symphony. *The number of completed, numbered symphonies by Johannes Brahms. *The number of strings on a violin, a viola, a cello, double bass, a cuatro (instrument), cuatro, a typical bass guitar, and a ukulele, and the number of string pairs on a mandolin. *"Four calling birds" is the gift on the fourth day of Christmas in the carol "The Twelve Days of Christmas (song), The Twelve Days of Christmas".


Groups of four

* Big Four (disambiguation) *Four basic operations of arithmetic:
addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol ) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication and Division (mathematics), division. ...
,
subtraction Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...
,
multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...
, division (mathematics), division. *Classical element#Classical elements in Greece, Greek classical elements (fire, air, water, earth). *Season, Four seasons: spring (season), spring, summer, autumn, winter. *The Four Seasons (disambiguation) *A leap year generally occurs every four years. *Approximately four weeks (4 times 7 days) to a lunar month (synodic month = 29.53 days). Thus the number four is universally an integral part of primitive sacred calendars. *Four weeks of Advent (and four Advent candles on the Advent wreath). *Four cardinal directions: north, south, east, west. *Four Temperaments: sanguine, choleric, Melancholia, melancholic, phlegmatic. *Humorism, Four Humors: blood, yellow bile, black bile, phlegm. *Four Great Ancient Capitals of China. *Four-corner method. *Four Asian Tigers, referring to the economies of Hong Kong, Taiwan, South Korea, and Singapore *Four cardinal principles, Cardinal principles. *Four cardinal virtues: justice, prudence, temperance, fortitude. *Four suit (cards), suits of playing cards: hearts, diamonds, clubs, spades. *Four nations of the United Kingdom: England, Wales, Scotland, Northern Ireland. *Four provinces of Ireland: Munster, Ulster, Leinster, Connacht. *Four estates: politics, public administration, administration, judiciary, journalism. Especially in the expression "Fourth Estate", which means journalism. *Four Corners Monument, Four Corners is the only location in the United States where four U.S. state, states come together at a single point: Colorado, Utah,
New Mexico ) , population_demonym = New Mexican ( es, Neomexicano, Neomejicano, Nuevo Mexicano) , seat = Santa Fe , LargestCity = Albuquerque , LargestMetro = Tiguex , OfficialLang = None , Languages = English, Spanish ( New Mexican), Navajo, Ker ...
, and Arizona. * Four Evangelists – Matthew the Apostle, Matthew, Mark the Evangelist, Mark, Luke the Evangelist, Luke, and John the Evangelist, John * Four Doctor of the Church, Doctors of Western Church – Saint Gregory the Great, Saint Ambrose, Saint Augustine, and Saint Jerome * Four Doctors of Eastern Church – Saint John Chrysostom, Saint Basil the Great, and Gregory of Nazianzus and Saint Athanasius * Four
Galilean moons The Galilean moons (), or Galilean satellites, are the four largest moons of Jupiter: Io, Europa, Ganymede, and Callisto. They were first seen by Galileo Galilei in December 1609 or January 1610, and recognized by him as satellites of Jupiter ...
of Jupiter – Io (moon), Io, Europa (moon), Europa, Ganymede (moon), Ganymede, and Callisto (moon), Callisto * The
Gang of Four The Gang of Four () was a Maoist political faction composed of four Chinese Communist Party (CCP) officials. They came to prominence during the Cultural Revolution (1966–1976) and were later charged with a series of treasonous crimes. The gang ...
was a Communist Party of China, Chinese communist political faction. * The Fantastic Four: Mr. Fantastic, The Invisible Woman, The Human Torch, The Thing. * The Teenage Mutant Ninja Turtles: Leonardo, Michelangelo, Donatello, Raphael * The Beatles were also known as the "Fab Four": John Lennon, Paul McCartney, George Harrison, Ringo Starr. * Gang of Four (band), Gang of Four is a British post-punk rock and roll, rock band formed in the late 1970s. * Four rivers in the Garden of Eden (Book of Genesis, Genesis 2:10–14): Pishon (perhaps the Jaxartes or Syr Darya), Gihon (perhaps the Oxus or Amu Darya), Hiddekel (Tigris), and P'rat (Euphrates). * There are also four years in a single Olympiad (duration between the Olympic Games). Many major international sports competitions follow this cycle, among them the FIFA World Cup and its FIFA Women's World Cup, women's version, the FIBA World Championships for FIBA World Championship, men and FIBA World Championship for Women, women, and the Rugby World Cup. * There are four limbs on the human body. * Four Houses of Hogwarts in the Harry Potter series: Gryffindor, Hufflepuff, Ravenclaw, Slytherin. * Four known continents of the world in the ''A Song of Ice and Fire'' series: Westeros, Essos, Sothoryos, Ulthos. * Each Grand Prix in Nintendo's ''Mario Kart'' series is divided into four cups and each cup is divided into four courses. The Mushroom Cup, Flower Cup, Star Cup, and Special Cup make up the Nitro Grand Prix, while the Shell Cup, Banana Cup, Leaf Cup, and the Lightning Cup make up the Retro Grand Prix.


See also

*List of highways numbered 4


References

*Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 55–58


External links


Marijn.Org on Why is everything four?
by Penelope Merritt at samuel-beckett.net
The Number 4The Positive Integer 4
{{Authority control Integers 4 (number),