This article may contain excessive, poor or irrelevant examples. You can improve the article by adding more descriptive text. See Wikipedia's guide to writing better articles for further suggestions. (March 2010) "Four" redirects here. For other uses, see Four (disambiguation). 4 −1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 → Cardinal 4 four Ordinal 4th fourth Numeral system quaternary Factorization 22 Divisors 1, 2, 4 Roman numeral IV or IIII Roman numeral (Unicode) Ⅳ, ⅳ Arabic ٤,4 Arabic (Persian, Urdu) ۴ Ge'ez ፬ Bengali ৪ Chinese numeral 四，亖，肆 Devanagari ४ Malayalam ൪ Tamil ௪ Hebrew ארבע (Arba, pronounced are-buh) or ד (Dalet, 4th letter of the Hebrew alphabet) Khmer ៤ Thai ๔ prefixes tetra- (from Greek) quadri-/quadr- (from Latin) Binary 100 Octal 4 Duodecimal 4 Hexadecimal 4 Vigesimal 4 Look up four in Wiktionary, the free dictionary. 4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5. Contents 1 In mathematics 1.1 List of basic calculations 2 Evolution of the glyph 3 In religion 4 In science 4.1 In astronomy 4.2 In biology 4.3 In chemistry 4.4 In physics 5 In logic and philosophy 6 In technology 7 In transport 8 In sports 9 In other fields 10 In music 11 Groups of four 12 References 13 External links In mathematics Four is the smallest composite number, its proper divisors being 1 and 2. Four is also a highly composite number. The next highly composite number is 6. Four is the second square number, the second centered triangular number. 4 is the smallest squared prime (p2) and the only even number in this form. It has an aliquot sum of 3 which is itself prime. The aliquot sequence of 4 has 4 members (4, 3, 1, 0) and is accordingly the first member of the 3-aliquot tree. Only one number has an aliquot sum of 4 and that is squared prime 9. The prime factorization of four is two times two. Four is the smallest composite number that is equal to the sum of its prime factors. (As a consequence of this, it is the smallest Smith number). However, it is the largest (and only) composite number n for which is false. It is also a Motzkin number. In bases 6 and 12, 4 is a 1-automorphic number. 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. A four-sided plane figure is a quadrilateral (quadrangle) or square, sometimes also called a tetragon. A circle divided by 4 makes right angles. Because of it, four (4) is the base number of plane (mathematics). Four cardinal directions, four seasons, duodecimal system, and vigesimal system are based on four.

A solid figure with four faces is a tetrahedron. 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. Four-dimensional space is the highest-dimensional space featuring more than three convex regular figures: Two-dimensional: infinitely many convex regular polygons. Three-dimensional: five convex regular polyhedra (the five Platonic Solids). Four-dimensional: six convex regular polychora. Five-dimensional and every higher-dimensional: three regular convex polytopes (regular simplexes, hypercubes, cross-polytopes). Four-dimensional differential manifolds have some unique properties. There is only one differential structure on except when n = 4, 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 maximum number of dimensions of a real division algebra (the quaternions), 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.1 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 numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares. Four is the first positive non-Fibonacci number. Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y2 − z2. Four is an all-Harshad number and a semi-meandric number. List of basic calculations Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 200 400 4000 Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 2 1 0.8 0.5 0.4 0.25 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 1 16 81 256 625 1296 2401 4096 6561 10000 14641 20736 28561 Evolution of the glyph Representing 1, 2 and 3 in as many lines as the number represented worked well. The Brahmin Indians simplified 4 by joining its four lines into a cross that looks like our modern plus sign. The Sunga would add a horizontal line on top of the numeral, and the Kshatrapa and Pallava evolved the numeral to a point where speed of writing was a secondary concern. The Arabs' 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 numeral less cursive, ending up with a glyph very close to the original Brahmin cross.2

While the shape of the 4 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in . On the seven-segment displays of pocket calculators and digital watches, as well as certain optical character recognition fonts, 4 is seen with an open top. This is because this was the original way the glyph was drawn (before the illustration above came into usage). Television stations 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". Another form of the 4 glyph that was invented for television was the arrow 4, which combines the 4 glyph with an arrow. In religion Buddhism Four Noble Truths Dukkha – The Noble Truth of Suffering Samudaya – The Noble Truth of the Cause of Suffering Nirodha – The Noble Truth of the Cessation of Suffering Magga – The Noble Truth of the Path leading to the Cessation of Suffering 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 man, a sick man, a dead man, and an ascetic Four Great Elements – earth, water, fire, 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 jhānas Four arūpajhānas Four Divine Abidings – loving-kindness, compassion, sympathetic joy, and equanimity Four stages of enlightenment – stream-enterer, once-returner, non-returner, and arahant Four main pilgrimage sites – Lumbini, Bodh Gaya, Sarnath, and Kusinara Judeo-Christian symbolism The Tetragrammaton is the four-letter name of God. The four Matriarchs (foremothers) of Judaism are Sarah, Rebeccah, Leah, and Rachel. The Four Species (lulav, hadass, aravah and etrog) are taken as one of the mitzvot on the Jewish holiday of Sukkot. (Judaism) The Four Cups of Wine to drink on the Jewish holiday of Passover. (Judaism) The Four Questions to be asked on the Jewish holiday of Passover. (Judaism) The Four Sons to be dealt with on the Jewish holiday of Passover. (Judaism) The Four Expressions of Redemption to be said on the Jewish holiday of Passover. (Judaism) The Four Horsemen of the Apocalypse ride in the Book of Revelation. The four Gospels: Matthew, Mark, Luke, and John. Hinduism In Puruṣārtha there are 4 aims of human life Dharma, Artha, Kāma, Moksha The four stages of life Brahmacharya (student life), Grihastha (household life), Vanaprastha (retired life) and Sannyasa (renunciation). The four primary castes or strata of society Brahmana (priest/teacher), Kshatriya (warrior/politician), Vaishya (landowner/entrepreneur) and Shudra (servant/manual laborer) Islam Eid al-Adha lasts for four days, from the 10th to the 14th of Dhul Hijja. There are four The Rightly Guided Caliphs or Rashidun: 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 Sacred Months in Islam: Muharram, Rajab, Dhu al-Qi'dah and Dhu al-Hijjah. There are four Sunni schools of fiqh: Hanafi, Shafi`i, Maliki and Hanbali. There are four major sunni Imams: Abū Ḥanīfa, Muhammad ibn Idris ash-Shafi`i, Malik ibn Anas and Ahmad ibn Hanbal. Other Four is the sacred number of the Zia, an indigenous tribe located in the U.S. State of New Mexico. The Chinese, Vietnamese, the Korean and the Japanese are superstitious about the number four because it is a homonym for "Death" in their languages In science A tetramer is a thing formed out of four sub-units. In astronomy Four terrestrial (or rocky) planets in the Solar system: Mercury, Venus, Earth, Mars. Four giant gas planets in the Solar system: Jupiter, Saturn, Uranus, Neptune. Four of Jupiter's moons (the Galilean moons) are readily visible from Earth. Messier object M4, a magnitude 7.5 globular cluster in the constellation Scorpius. The New General Catalogue object NGC 4, a faint galaxy in the constellation Pisces The Roman numeral IV stands for subgiant in the Yerkes spectral classification scheme. The Roman numeral IV (usually) stands for the fourth-discovered satellite of a planet or minor planet (e.g. Jupiter IV) In biology Four is the number of nucleobase types in DNA and RNA – adenine, guanine, cytosine, thymine (uracil in RNA). Many chordates have four feet, legs or leglike appendages (Tetrapods). The mammalian heart consists of four chambers. Many mammals (Carnivora, Ungulata) use four fingers for movement. The fourth finger of a human hand (on the left hand – ring-finger) is moved when the little finger moves. All insects with wings except flies have four wings. 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. There are four human blood groups (A, B, O, AB). Humans have four canines, four incisors and four wisdom teeth. The cow's stomach is divided in four digestive compartments: reticulum, rumen, omasum and abomasum. In 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. The four elements of alchemy are earth, water, air and fire. In physics Special relativity and general relativity treat nature as four-dimensional – time and three-dimensional space 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). An alpha particle (helium nucleus, also called a helion) consists of four hadrons. 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"..."lord of the four quarters of the earth"... by which is understood 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 distinct possibilities: the propositions are subalterns (both can be true and both can be false); subcontraries (both of them can be true but cannot both be false); contraries (both of them can be false but cannot both be true); or contradictories (both of them cannot be true and cannot both be false). Aristotle held that there are basically four causes in nature: the efficient cause, the matter, the end, and the form. The Stoics 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. Immanuel Kant 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. 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.) C. S. Peirce, usually a trichotomist, discussed four basic methods of seeking to settle questions and arrive at firm beliefs: (1) the method of tenacity (sticking to one's initial belief), (2) the method of authority, (3) the a priori method, and (4) the 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 (see "F.R.L." (First Rule of Logic), 1899). Paul Weiss 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). 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 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 "tropes"). (See Lowe's "Recent Advances in Metaphysics," 2001, Eprint) In technology The resin identification code used in recycling to identify low-density polyethylene. Most furniture has four legs – tables, chairs, etc. Four horses (quadriga) is the maximal number of horses in one row for carriage. The four color process (CMYK) is used for printing. Wide use of rectangles (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 4 mod 256. 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 cellular phone, 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 bits 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". In Leetspeak, "4" may be used to replace the letter "A". In transport Most vehicles, including motor vehicles, and particularly cars/automobiles and light commercial vehicles have four road wheels. "quattro", meaning four in the Italian language, is used by Audi as a trademark to indicate that four-wheel drive (4WD) 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. The designation of Interstate 4, a freeway in Florida, the lowest unqualified number assigned and signed in the Interstate Highway System of the United States. (There is an Interstate H-1, Interstate H-2 and Interstate H-3 in Hawaii.) In sports In cricket, 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). In basketball, the term Final Four refers to the last four teams remaining in the NCAA playoff tournament, each of which is the winner of its respective region In 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 baseball scoring, number 4 is assigned to the second baseman. In gridiron football codes, four points are awarded in a handful of leagues for rarely attempted types of field goals; an example is in six-man football. Because of the difficulties of getting a successful kick due to the few players on the field, a field goal is worth four points. Also, in Arena Football, a successful dropkicked field goal attempt scores four points. the "four hole" in offense terminology is the space between the right guard and the right tackle on the offensive line the "four back" is an extra running back (outside the fullback and halfback, often referred to as an H-back) in the backfield; e.g. a play call for a "44 lead" indicates the H-back will follow the fullback into the hole between the right guard and the right tackle. In other fields International maritime signal flag for 4

See also 4 (disambiguation). The phrase "four-letter word" is used to describe most swear words in the English language, as most swear words do indeed possess four letters. Four (四, formal writing: 肆, pinyin sì) is considered an unlucky number in Chinese, Korean, Vietnamese and Japanese cultures because it sounds like the word "death" (死, pinyin sǐ). Due to that, many numbered product lines skip the "four": e.g. Nokia cell phones (there is no series beginning with a 4), Microsoft Windows (which switched to "Windows 95" for version 43), Palm PDAs, the Leisure Suit Larry games, 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". In Astrology, Cancer is the 4th astrological sign of the Zodiac. In Tetris, a game named for the Greek word for 4, every shape in the game is formed of 4 blocks each. 4 is one of The Numbers – 4, 8, 15, 16, 23, and 42 – featured in Lost. 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). In music In classical music, common time is constructed of four beats. The 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, an album by Blues Traveler 4, an album by Foreigner Groups of four Four rules: addition, subtraction, multiplication, division. Greek classical elements (fire, air, water, earth). Four seasons: spring, summer, autumn, winter. Four parts of a day: night, morning, afternoon, evening. Four cardinal directions: north, south, east, west. Four Temperaments: sanguine, choleric, melancholic, phlegmatic. Four Humors: blood, yellow bile, black bile, phlegm. Four Great Ancient Capitals of China Four corner method Cardinal principles Four canonical Christian Gospels, attributed to the Four Evangelists (Matthew, Mark, Luke, and John) Four horsemen of the Apocalypse: war, famine, pestilence, death. Four suits of playing cards: hearts, diamonds, clubs, spades. Four nations of the United Kingdom: England, Wales, Scotland, Northern Ireland. Four Noble Truths in the Buddhist religion. Four estates: politics, administration, judiciary, journalism. Especially in the expression "Fourth Estate", which means journalism. Four Corners is the only location in the United States where four states come together at a single point: Colorado, Utah, New Mexico, and Arizona. The Fantastic Four: Mr. Fantastic, The Invisible Woman, The Human Torch, and The Thing. The Beatles were also known as the "Fab Four": John Lennon, Ringo Starr, George Harrison, and Paul McCartney. Gang of Four is a British post-punk rock band formed in the late 1970s. Typically there are four string players in a classical string quartet, usually two violinists, a violist, and a cellist. Four rivers in the Garden of Eden (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). The World Cup is held at every four years. References ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 48 ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.64 ^ http://windowsteamblog.com/blogs/windowsvista/archive/2008/10/14/why-7.aspx Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 55 - 58 External links Wikimedia Commons has media related to: 4 (number) Marijn.Org on Why is everything four? A few thoughts on the number four, by Penelope Merritt at samuel-beckett.net