4

4
Template:Numbers (digits)
Cardinal	4 four
Ordinal	4th fourth
Numeral system	quaternary
Factorization	$2^{2}$
Divisors	1, 2, 4
Roman numeral	IV or IIII
Roman numeral (Unicode)	Ⅳ, ⅳ
Arabic	٤
Arabic (Urdu)	۴
Ge'ez	፬
Bengali	৪
Chinese numeral	四，亖，肆
Devanagari	४
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

This article discusses the number Four. For the year 4 AD, see 4. For other uses of 4, see 4 (disambiguation)

4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5. Four is the only number in the English language for which the number of letters in its name is equal to the number itself. This is also true in several other languages, such as German, Afrikaans, Dutch, and Flemish, as "vier".

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 ($p^{2}$). It has an aliquot sum of 3 which is itself prime. The aliquot sequence of 4 has 4 members (4,3,1,0).

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 $(n-1)!\ \equiv \ 0\ ({\rm {mod}}\ n)$ is false.

It is also a Motzkin number.

In addition, $2+2=2\times 2=2^{2}=4$. Continuing the pattern in Knuth's up-arrow notation, $2\uparrow \uparrow 2=2\uparrow \uparrow \uparrow 2=4$, 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 has the largest number of dimensions used by more than three convex regular figures. There are infinitely many convex regular polygons (two-dimensional); five convex regular polyhedra (three-dimensional, the five Platonic Solids); six convex regular polychora (four-dimensional); and three regular convex polytopes occupying each higher-dimensional space.

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. 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. $4x=y^{2}-z^{2}.$

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
$4\times x$	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
$4\div x$	4	2	$1.{\overline {3}}$	1	0.8	$0.{\overline {6}}$	$0.{\overline {5}}7142{\overline {8}}$	0.5	$0.{\overline {4}}$	0.4		$0.{\overline {3}}{\overline {6}}$	$0.{\overline {3}}$	$0.{\overline {3}}0769{\overline {2}}$	$0.{\overline {2}}8571{\overline {4}}$	$0.2{\overline {6}}$
$x\div 4$	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

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13
$4^{x}\,$	4	16	64	256	1024	4096	16384	65536	262144	1048576		4194304	16777216	67108864
$x^{4}\,$	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 represents worked well enough, but writing four lines proved tiresome. The Brahmin Indians simplified 4 by joining its four lines into a cross that looks like our modern plus sign. The Sunga and other Indians 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 at best a secondary concern. The Arabs didn't have time for cursive fancy: their 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 off the finishing curve and gradually made the numeral less cursive, ending up with a glyph very close to the original Brahmin cross.

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, 4 is seen with an open top.

 

In religion

• The Tetragrammaton is the four-letter name of God.
• The four Matriarchs (foremothers) of Judaism are Sarah, Rebeccah, Leah, and Rachel.
• The Four Arch Angels in Islam are: Jibraeel (Gabriel), Mikaeel (Michael), Izraeel (Azrael), and Israfil (Raphael)
• 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.
• Four is the sacred number of the Zia, an indigenous tribe located in the United States State of New Mexico.
• The Chinese and the Japanese are superstitious about the number four because it is a homonym for "Death" in their languages
• The Four Noble Truths of Buddhism.
• The four Gospels: Matthew, Mark, Luke, and John.

In science

In astronomy

• The orbits of four planets in the solar system lie within that of the asteroid belt.
• 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 Saros number of the solar eclipse series which began on -2731 May 6 and ended on -1451 June 13. The duration of Saros series 4 was 1280.1 years, and it contained 72 solar eclipses.
• The Saros number of the lunar eclipse series which began on -2700 September 3 and ended on -1131 April 2. The duration of Saros series 4 was 1568.6 years, and it contained 88 lunar eclipses.
• 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.
• Butterflies and dragonflies have four wings.
• There are four human blood groups (A, B, O, AB).
• People have four canines, four incisor and four wisdom teeth.

In chemistry

• Valency of carbon (that is basis of life on the Earth) is four. Thanks to 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.

In physics

• Special relativity and general relativity treats nature as four-dimensional — time and three-dimensional space are treated together and called spacetime.
• An alpha particle (helium nucleus, also called a helion) consists of four hadrons.
• There are four fundamental forces (electromagnetism, gravity, the weak nuclear force, and the strong nuclear force).

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").
• Aristotle held that there are basically four causes in nature: the efficient cause, the matter, the end, and the form.
• 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.
• C.S. Peirce, usually a trichotomist, discussed four basic methods of seeking to settle questions and arrive at firm beliefs: the method of tenacity (sticking to that which one is inclined to think), the method of authority, the a priori method, and the method of science. (See "The Fixation of Belief," 1877, Eprint.)
• Jonathan Lowe (E.J. Lowe) argues in The Four-Category Ontology, 2006, for four categories: objects, attributes, kinds, and modes (by "modes" he means property-particulars, also known as "tropes"). (See Lowe's "Recent Advances in Metaphysics," 2001, Eprint)

In technology

4 as a resin identification code, used in recycling.

• 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 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 Expressing love, "4" may be used to replace the word "Love" (143).

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.

In sports

• In the sport of cricket, a four is a specific type of scoring event, scoring four runs.

• In rugby union, the number of the lock forward, who usually jumps at number 2 in the line-out.

• In rugby league, the number of one of the two centres. It is also the number of points awarded for a try.

• In baseball, 4 represents the second baseman's position.

• In basketball, 4 represents the power forward position. Also, The term Final Four refers to the last four teams remaining in the NCAA playoff tournament. If a player completes a three-pointer while being fouled, the player is awarded one free-throw for a possible 4-point-play.

• In rowing, a four refers to a boat for four rowers, with or without coxswain. In rowing nomenclature 4- reprsents a coxless four and 4+ represents a coxed four.

• In football (soccer), number 4 is often assigned to a centre back.

In other fields

International maritime signal flag for 4

See also 4 (disambiguation).

• A four-letter word is used to describe most swear words in the English language, as most such terms do indeed possess four letters.
• Four (四, formal writing: 肆, pinyin sì) is considered an unlucky number in Chinese, Korean, 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), 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.
• In the NATO phonetic alphabet, the digit 4 is called "fower".
• The number of characters in a canonical four-character idiom.
• 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.
• The designation of Interstate 4, a freeway in Florida.
• The number of arms possessed by video game villain Goro.
• Four, an album by Blues Traveler
• 4, an album by Foreigner
• The number of completed, numbered symphonies by Johannes Brahms
• In Astrology, Cancer is the 4th astrological sign of the Zodiac.
• 4 is one of The Numbers - 4, 8, 15, 16, 23, and 42 - featured in Lost.
• Arthur Conan Doyle wrote a book titled "The Sign of Four"
• In Tetris, every shape in the game is formed of 4 blocks each. Also the game was named after "tetra" the Greek word for 4.

In Music

In Western Music, common time is constructed of four beats.

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.
• Typically there are four movements in a classical symphony or string quartet.
• The Beatles were also known as the 'Fab Four': John Lennon, Ringo Starr, George Harrison, and Paul McCartney.
• The Gang of Four was a group of Communist Party leaders in the People's Republic of China who were blamed for the Cultural Revolution.
• Gang of Four is a British post-punk rock band formed in the late 1970s.
• There are also four members in a quartet. See also List of musical quartets.
• Four food groups (Meat products, dairy products, grain products, and fruits/vegetables). Note that this traditional model is falling out of favour, as fruits and vegetables became separate groups in the 1992 USDA food guide pyramid. Also, refined fats and sugars constitute another group (traditionally considered non-essential).
• 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)

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?
• A few thoughts on the number four, by Penelope Merritt at samuel-beckett.net