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Four Great Elements – earth, water, fire, and wind.

Four sights – observations which affected Prince Siddhartha deeply and made him realize the sufferings of all beings, and compelled him to begin his spiritual journey-an old man, a sick man, a dead man, and an ascetic.

Four Noble Truths – Dukkha, Samudaya, Nirodha, Magga.The magnetic ink character recognition "CMC-7" font also uses this variety of "4". This version resembles the Canadian Aboriginal syllabics letter ᔦ. 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. 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. List of basic calculations Multiplication 4 x = y 2 − z 2.įour is the highest degree general polynomial equation for which there is a solution in radicals.

Įach natural number divisible by 4 is a difference of squares of two natural numbers, i.e. Three are not always sufficient 7 for instance cannot be written as the sum of three squares. Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square numbers. The largest planar complete graph has four vertices. Three colors are not, in general, sufficient to guarantee this. 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. Four is also the order of the smallest non-trivial groups that are not simple.įour is the only integer n for which the (non trivial) alternating group A n is not simple.įour is the maximum number of dimensions of a real associative division algebra (the quaternions), by a theorem of Ferdinand Georg Frobenius. The smallest non- cyclic group has four elements it is the Klein four-group. There is only one differential structure on R n except when n = 4, in which case there are uncountably many.

Five-dimensional and every higher-dimensional: three regular convex polytopes ( regular simplexes, hypercubes, cross-polytopes).įour-dimensional differential manifolds have some unique properties.

Four-dimensional: six convex regular polychora.

Three-dimensional: five convex regular polyhedra (the five Platonic solids).

Two-dimensional: infinitely many convex regular polygons.

įour-dimensional space is the highest-dimensional space featuring more than three convex regular figures: It is the only self-dual regular polyhedron. A tetrahedron, which can also be called a 3- simplex, has four triangular faces and four vertices. The regular tetrahedron is the simplest Platonic solid.

It can be further classified as a rectangle, oblong, square, kite, or rhombus.Ī 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. (That is, 2 2 = 4 for every positive integer n, where a b is the hyperoperation.)Ī four-sided plane figure is a quadrilateral (quadrangle), sometimes also called a tetragon. Continuing the pattern in Knuth's up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so on, for any number of up arrows. For example, 1092 is a multiple of 4 because 92 = 4 × 23. 4 is also the only square one more than a prime number.Ī number is a multiple of 4 if its last two digits are a multiple of 4. Ĥ is the smallest squared prime ( p 2) and the only even number in this form. Four is the smallest composite number, its proper divisors being 1 and 2.