4"/40 caliber gun

← 3 4 5 →
-1 0 1 2 3 4 5 6 7 8 9
Cardinal four
Ordinal 4th
(fourth)
Numeral system quaternary
Factorization 22
Divisors 1, 2, 4
Greek numeral Δ´
Roman numeral IV
Roman numeral (unicode) Ⅳ, ⅳ
Greek prefix tetra-
Latin prefix quadri-/quadr-
Binary 1002
Ternary 113
Quaternary 104
Quinary 45
Senary 46
Octal 48
Duodecimal 412
Hexadecimal 416
Vigesimal 420
Base 36 436
Greek δ (or Δ)
Arabic, Saraiki & Kurdish ٤
Persian ۴
Urdu ۴
Ge'ez
Bengali
Chinese numeral 四,亖,肆
Korean 넷,사
Devanagari
Telugu
Malayalam
Tamil
Hebrew ד
Khmer
Thai
Kannada
Burmese

4 (four; /fɔːr/) 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 1 and 2.

4 is the smallest squared prime (p2) 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 92 = 4 × 23.

In addition, 2 + 2 = 2 × 2 = 22 = 4. Continuing the pattern in Knuth's up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so on, for any number of up arrows. (That is, 2 [n] 2 = 4 for every positive integer n, where a [n] b is the hyperoperation.)

A four-sided plane figure is a quadrilateral (quadrangle) which include kites, rhombi, rectangles and squares, sometimes also called a tetragon. A circle divided by 4 makes right angles and four quadrants. Because of it, four (4) is the base number of the plane (mathematics). Four cardinal directions, four seasons, the duodecimal system, and the vigesimal system are based on four.

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.

Four-dimensional space is the highest-dimensional space featuring more than three convex regular figures:

Four-dimensional differential manifolds have some unique properties. There is only one differential structure on ℝn 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 only integer n for which the (non trivial) alternating group An is not simple.

Four is the maximum number of dimensions of a real associative 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.

Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y2z2.

Four is the highest degree general polynomial equation for which there is a solution in radicals.

The four fours game, there are known solutions for all integers from 0 to 880 (but not 881).[citation needed]

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 × 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 16
4 ÷ x 4 2 1.3 1 0.8 0.6 0.571428 0.5 0.4 0.4 0.36 0.3 0.307692 0.285714 0.26 0.25
x ÷ 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 4
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
4x 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864
x4 1 16 81 256 625 1296 2401 4096 6561 10000 14641 20736 28561

Evolution of the glyph[]

Evolution4glyph.png

Representing 1, 2 and 3 in as many lines as the number represented worked well.[citation needed] The Brahmin Indians simplified 4 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 numeral, and the Kshatrapa and Pallava evolved the numeral to a point where the 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 TextFigs148.svg.

Seven-segment 4.svg

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.

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 or the Coptic letter Ϥ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4".

In religion[]

Buddhism[]

Judeo-Christian symbolism[]

Hinduism[]

Islam[]

Taoism[]

Other[]

In politics[]

In computing[]

In science[]

In astronomy[]

In biology[]

In chemistry[]

In physics[]

In logic and philosophy[]

In technology[]

4 as a resin identification code, used in recycling.

In transport[]

BKV m 4 jms.svg

In sports[]

In other fields[]

In music[]

Albums[]

Groups of four[]

References[]

  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 48
  2. ^ 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
  3. ^ Chevalier, Jean and Gheerbrant, Alain (1994), The Dictionary of Symbols. The quote beginning "Almost from prehistoric times..." is on p. 402.

External links[]