4 (number)

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

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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
prefixes tetra- (from Greek)

quadri-/quadr- (from Latin)
Binary 100
Octal 4
Duodecimal 4
Hexadecimal 4
Vigesimal 4
Hebrew ד (Daled)
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

[edit] 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.

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, a website is dedicated to this subject

- Dutch Marijn.Org on Why is everything four?

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 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.

4 is the supreme number of the universe according to the Time Cube (see Time Cube#Mathematical claims).

[edit] 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

[edit] Evolution of the glyph

Image:Evolution4glyph.png

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.

In fonts with text figures, 4 usually has a descender, for example, Image:TextFigs148.png.

[edit] In religion

[edit] In science

[edit] In astronomy

[edit] In biology

[edit] 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

[edit] In physics

[edit] In technology

  • Most furniture has four legs - tables, chairs, etc.
  • Four horses (quadriga) is the maximal number of horses in one row for carriage.
  • 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).
  • 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.
  • Some computer users may use "4" as an alternate to the letter "A", example "c4r" is alternate to the word "car", often in jest or to prevent search engines from reading their messages. This form of code is an example of basic Leetspeak.
  • Some computer users may use "4" as an alternate (for shortly when typing) to the word "for", because "four" and "for" may same sound when speaking, and use "4u" as an alternate of "for you".

[edit] In sports

Four positions of a pitch in baseball
Enlarge
Four positions of a pitch in baseball

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. It was the jersey number of Earl Weaver, long-time manager of the Baltimore Orioles.

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.

Once Favre retires, the Packers are expceted to retire Favre's jersey. This will cause 4 to be the first number to be retired by all the major professional sports franchises in a single U.S. state (Wisconsin) as the Milwaukee Brewers have retired the number for Molitor and the Milwaukee Bucks have retired it in honor of Sidney Moncrief.

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

[edit] In other fields

See also 4 (disambiguation)

[edit] Groups of four

Enlarge

[edit] Historical years

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

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