4 (number)

This article discusses the number Four. For the year 4 AD, see 4. For other uses of 4, see 4 (disambiguation) quadri-/quadr- (from Latin)


Cardinal	4 four
Ordinal	4th fourth
Numeral system	quaternary
Factorization	$2^2$
Divisors	1, 2, 4
Roman numeral	IV or IIII
Unicode representation of Roman numeral	Ⅳ, ⅳ
prefixes	tetra- (from Greek)
Binary	100
Octal	4
Duodecimal	4
Hexadecimal	4
Vigesimal	4
Hebrew	ד (Dalet)

4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5.

In mathematics

Four is the smallest composite number, its proper divisors being and . Four is also a highly composite number. The next highly composite number is . Four is the second square number, the second centered triangular number.

Four is the only number in the English language for which the number of letters in its name is equal to the number itself.

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.

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.

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.

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.

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 number of n-Queens Problem solutions for n = 6.

There are four basic arithmetic operations: addition, subtraction, multiplication and division.

The Cartesian coordinate system for a plane has four quadrants.

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.

The Arabic glyph

Representing 1, 2 and 3 in as many lines as the number represents worked well enough, but with 4 writing four lines began to appear 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.

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 Species (lulav, hadass, aravah and etrog) are taken as one of the mitzvot on Sukkot

In science

In physics

There are four fundamental forces of nature: gravity, the strong nuclear force, the weak nuclear force, and the electromagnetic force.

Special relativity and general relativity treats nature as four-dimensional — time and three-dimensional space are treated together and called spacetime.

Alpha particle (helium nucleus) consists of four hadrons.

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

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 (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.

People have four canines, four incisor and four wisdom teeth.

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 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.

In technology

Most vehicles have four wheels.

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 computer keyboards, the "4" key may also be used to type the dollar sign (^*]) if the shift key is held down.

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. It was also the jersey number of Lou Gehrig, Mel Ott, Joe Cronin, and Paul Molitor.

In basketball, 4 represents the power forward position.

In ice hockey, 4 was the jersey number worn by Hall of Famers Jean Beliveau and Bobby Orr.

In American football, 4 is today most commonly identified with the jersey number of Green Bay Packers quarterback Brett Favre.

In rowing, a four refers to a boat for four rowers, with or without coxswain.

In other fields

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.
ancient capitals of China
Four corner method
cardinal principles
Four Evangelists : Matthew, Mark, Luke, John.
horsemen of the Apocalypse : war, famine, plague, death.
Four suits of playing cards : hearts, diamonds, clubs, spades.
The terrorist group known as 4 caused controversy on James Madison University's campus in 2004-2006.
The number of tines of most forks.
Four nations of the United Kingdom: England, Wales, Scotland, Northern Ireland.
Noble Truths in the Buddhist faith.
Four estates : politics, administration, judiciary, journalism. Especially in the expression "Fourth Estate", which means journalism.
There are 4 theme parks that make up the Walt Disney World resort in Orlando, Florida: the Magic Kingdom, Epcot, Disney-MGM Studios, and Disney's Animal Kingdom.
Four Corners is the only location in the United States where visitors can be in four separate states at one time: Colorado, Utah, New Mexico, and Arizona.
There were four Superman movies starring Christopher Reeve.
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 also four members in a quartet. See also List of musical quartets.

Historical years

A.D. 4, 4 B.C., 1904, 2004, etc.

Integers

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