4 (four) is a number
. It is the natural number
and preceding 5
. It is the smallest composite number
, and is considered unlucky
in many East Asian cultures.
Four is the smallest composite number
, its proper divisor
s being and .
4 is the smallest squared prime (''p''2
) and the only even number in this form. 4 is also the only square one more than a prime number.
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 .
In addition, 2 + 2 = 2 × 2 = 22
= 4. Continuing the pattern in Knuth's up-arrow notation
, , and so on, for any number of up arrows. (That is, for every positive integer ''n'', where is the hyperoperation
A four-sided plane figure is a quadrilateral
(quadrangle), sometimes also called a ''tetragon''. It can be further classified as a rectangle, oblong, square, kite, or rhombus.
A solid figure with four faces as well as four vertices is a tetrahedron
, and 4 is the smallest possible number of faces (as well as vertices) of a polyhedron
. The regular tetrahedron is the simplest Platonic solid
. A tetrahedron
, which can also be called a 3-simplex
, has four triangular faces and four vertices. It is the only self-dual regular polyhedron
is the highest-dimensional space featuring more than three convex regular figures:
*Two-dimensional: infinitely many convex regular polygon
*Three-dimensional: five convex regular polyhedra
(the five Platonic solid
*Four-dimensional: six convex regular polychora
*Five-dimensional and every higher-dimensional: three regular convex polytope
s (regular simplexes
Four-dimensional differential manifold
s have some unique properties. There is only one differential structure
except when , in which case there are uncountably many.
The smallest non-cyclic group
has four elements; it is the Klein four-group
. Four is also the order of the smallest non-trivial groups that are not simple
Four is the only integer ''n'' for which the (non trivial) alternating group
''A'' is not simple.
Four is the maximum number of dimensions of a real associative division algebra
), by a theorem
of Ferdinand Georg Frobenius
The four-color theorem
states that a planar graph
(or, equivalently, a flat map
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
has four vertices.
Lagrange's four-square theorem
states that every positive integer can be written as the sum of at most four square number
s. Three are not always sufficient; for instance cannot be written as the sum of three squares.
Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. .
Four is the highest degree general polynomial equation
for which there is a solution in radicals
List of basic calculations
Evolution of the Arabic digit
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
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
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
s, in typefaces with text figures
the glyph usually has a descender
, as, for example, in
On the seven-segment display
s of pocket calculators and digital watches, as well as certain optical character recognition
fonts, 4 is seen with an open top.
s that operate on channel 4
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
letter ᔦ. The magnetic ink character recognition
"CMC-7" font also uses this variety of "4".
*Four Noble Truths
– 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
man, a sick
man, a dead
man, and an ascetic
*Four Great Elements
, and wind
*Four Heavenly Kings
*Four Foundations of Mindfulness
– contemplation of the body, contemplation of feelings, contemplation of mind, contemplation of mental objects
*Four Right Exertions
*Four Bases of Power
*Four Divine Abidings
, sympathetic joy
, and equanimity
*Four stages of enlightenment
, and arahant
*Four main pilgrimage sites
, Bodh Gaya
, and Kusinara
is the four-letter name of God
has a vision of four living creatures
: a man, a lion, an ox, and an eagle.
*The four Matriarchs (foremothers) of Judaism
, and Rachel
*The Four Species
) are taken as one of the mitzvot
on the Jewish
holiday of Sukkot
*The Four Cups of Wine to drink on the Jewish
holiday of Passover
*The Four Questions to be asked on the Jewish
holiday of Passover
*The Four Sons to be dealt with on the Jewish
holiday of Passover
*The Four Expressions of Redemption to be said on the Jewish
holiday of Passover
*The four Gospel
, and John
*The Four Horsemen of the Apocalypse
ride in the Book of Revelation
*The Four Holy Cities
of Judaism: Jerusalem
, and Tiberius
*There are four Vedas
: Rigveda, Samaveda, Yajurveda and Atharvaveda.
, there are four aims of human life: Dharma
*The four stages of life Brahmacharya
(student life), Grihastha
(household life), Vanaprastha
(retired life) and Sannyasa
*The four primary castes or strata of society: Brahmana
(landowner/entrepreneur) and Shudra
symbol is traditionally used in Hindu
religions as a sign of good luck and signifies good from all four directions.
*The god Brahma
has four faces.
*There are four ''yuga
'' and ''Kali
lasts for four days, from the 10th to the 14th of Dhul Hijja
*There are four Rashidun
or Rightly Guided Caliph
s: Abu Bakr
, Umar ibn al-Khattab
, Uthman ibn Affan
and Ali ibn Abi Talib
*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
, Dhu al-Qi'dah
and Dhu al-Hijjah
*There are four Sunni
schools of fiqh
*There are four major Sunni Imams: Abū Ḥanīfa
, Muhammad ibn Idris ash-Shafi`i
, Malik ibn Anas
and Ahmad ibn Hanbal
*There are four books in Islam
: Torah, 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
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
of I Ching
*In a more general sense, numerous mythological and cosmogonical systems consider Four corners of the world
as essentially corresponding to the four points of the compass.
*Four is the sacred number of the Zia
, an indigenous tribe located in the U.S. state of New Mexico
*The Chinese, the Koreans, and the Japanese are superstitious about the number four
because it is a homonym
for "death" in their languages.
*In Slavic mythology
, the god Svetovid
has four heads.
: four fundamental freedoms that Franklin D. Roosevelt
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
: 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
. Among the four was Mao's widow, Jiang Qing
. Since then, many other political factions headed by four people have been called "Gangs of Four".
s (half a byte
) are sometimes called a nibble
is an oligomer
formed out of four sub-units.
*Four terrestrial (or rocky) planets in the Solar system
, and Mars
*Four giant gas/ice planets in the Solar system
, and Neptune
*Four of Jupiter's moons (the Galilean moons
) are readily visible from Earth with a hobby telescope.
*Messier object M4
, a magnitude 7.5 globular cluster
in the constellation Scorpius
*The Roman numeral IV stands for subgiant
in the Yerkes spectral classification scheme
*Four is the number of nucleobase
types in DNA
s have four feet, legs or leglike appendages (tetrapods
consists of four chambers.
) use four fingers for movement.
s with wings except flies
and mosquitos and some others have four wing
*Insects of the superorder Endopterygota
, also known as Holometabola, such as butterflies, ants, bees, beetles, fleas, flies, moths, and wasps, undergo holometabolism
—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
, there are 4 blood types (A, B, O, AB).
have four canines
and four wisdom teeth
*The cow's stomach is divided in four digestive compartments: reticulum, rumen, omasum and abomasum.
(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
*There are four basic states of matter
, and plasma
and general relativity
treat nature as four-dimension
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
, 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 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'' (it is possible that both are true, but not that both are false); ''contraries'' (it is possible that both are 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).
held that there are basically four causes
in nature: the material
, the formal
, the efficient
,and the final
held with four basic 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.
expounded a table of judgments
involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a table of four categories
, named by the terms just listed, and each with three subcategories.
's doctoral thesis was ''On the Fourfold Root of the Principle of Sufficient Reason
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.)
*C. S. Peirce
, usually a 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 fallibilistic
, self-correcting method of science (see "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 absolutely unknowable; (3) maintaining that something is absolutely inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (seeF.R.L. irst Rule of Logic
built a system involving four modes of being: Actualities (substances in the sense of substantial, spatio-temporally finite beings), Ideality or Possibility (pure normative form), Existence (the dynamic field), and God (unity). (See Weiss's ''Modes of Being'', 1958).
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 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.
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.)
(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 "tropes
"). (See Lowe's "Recent Advances in Metaphysics," 2001Eprint
*Four opposed camps of the morality and nature of evil: moral absolutism
, moral relativism
, and moral universalism
*The resin identification code
used in recycling to identify low-density polyethylene
has four legs – tables, chairs, etc.
*The four color process
) is used for printing
*Wide use of rectangle
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 .
machines have four-twelve function keys.
*On most phones, the 4 key is associated with the letters G
, and I
, but on the BlackBerry
cellular phone, it is the key for D
*On many computer keyboard
s, 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
s in a nibble
, equivalent to half a byte
*In internet slang
, "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you".
speak, "4" may be used to replace the letter "A".
*The TCP/IP stack
consists of four layers.
*Many internal combustion engines
are called four-stroke
engines because they complete one thermodynamic cycle in four distinct steps: Intake, compression, power, and exhaust.
s, including motor vehicle
s, and particularly cars/automobiles
and light commercial vehicle
s have four road wheel
", 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 the Australian Football League
, the top level of Australian rules football
, each team is allowed 4 "interchanges
" (substitute players), who can be freely substituted at any time, subject to a limit on the total number of substitutions.
**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 "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
, the number four is used to designate the power forward
position, often referred to as "the four spot" or "the four".
, a four is a specific type of scoring event, whereby the ball crosses the 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).
, 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
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 locks
wears the jersey number 4.
** In the standard 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 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
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
), Palm 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
*The number of characters in a canonical four-character idiom
*In the NATO phonetic alphabet
, the digit 4 is called "fower".
is the 4th astrological sign
of the Zodiac
, The Emperor
is the fourth trump
or Major Arcana
'', 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).
*Number Four is a character in the book series ''Lorien Legacies
*In written music
, common time
is constructed of four beats per measure and a quarter note receives one beat.
*In popular or modern music
, the most common time signature
is also founded on four beats, i.e., 4/4 having four quarter note
*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
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
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
'', British rock band Bloc Party
's fourth full-length album.
'', British-Irish boy band One Direction
's fourth full-length album.
'', American artist Beyoncé
's fourth album.
'', British–American band Foreigner
's fourth studio album.
Groups of four
* Big Four (disambiguation)
*Four basic operations of arithmetic: addition
*Greek classical elements
*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 candle
s on the Advent wreath
*Four cardinal directions
, yellow bile
, black bile
*Four Great Ancient Capitals of China
*Four cardinal virtues
: justice, prudence, temperance, fortitude.
of playing card
s: hearts, diamonds, clubs, spades.
s of the United Kingdom
: England, Wales
, Northern Ireland
*Four provinces of Ireland
*Four estates: politics
. Especially in the expression "Fourth Estate
", which means journalism.
is the only location in the United States where four states
come together at a single point: Colorado
, New Mexico
, and Arizona
* Four Evangelists
, and John
* Four 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
of Jupiter – Io
, and Callisto
* The Gang of Four
was a Chinese communist
* The Fantastic Four
: Mr. Fantastic, The Invisible Woman, The Human Torch, The Thing.
* The Teenage Mutant Ninja Turtles
: Leonardo, Michelangelo, Donatello, Raphael
* The Interesting Four
: Seiko, The Human Stapler, Weather Woman, and Mr. Wonderful. Parody superhero team featured on NBC's ''Saturday Night Live
* The Beatles
were also known as the "Fab Four": John Lennon, Ringo Starr, George Harrison, Paul McCartney.
* Gang of Four
is a British post-punk rock
band formed in the late 1970s.
* Four rivers in the Garden of Eden
(perhaps the Jaxartes or Syr Darya
(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 women's version
, the FIBA World Championships for men
, and the Rugby World Cup
* There are four limbs on the human
* 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.
*List of highways numbered 4
*Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers
'' London: Penguin Group. (1987): 55–58
Marijn.Org on Why is everything four?
by Penelope Merritt at samuel-beckett.netThe Number 4The Positive Integer 4