4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5.
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 first non-unitary square prime (2^2). It has a aliquot sum σ(n) 3 which is itself a prime. The aliquot sequence of 4 has 4 members (4,3,1,0) this number being the 1st composite member of the 3-aliquot tree.
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. 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. It is the only self-dual regular polyhedron. 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 = y2 − z2. Four is an all-Harshad number and a semi-meandric number.
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 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.
* 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". |
