The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of the Pythagorean school, it was the number of justice. The sacred tetraktýs (10) was the sum of the first four numbers, depicted as a triangle with two equal sides of length 4.

4 is the highest degree for which an algebraic equation is always solvable by radicals. It is the smallest order of a field which is not a prime field, and the smallest order for which there exist two nonisomorphic finite groups (finite group C2×C2 and the cyclic group C4). It is the smallest number of faces of a regular polyhedron, the tetrahedron. In the three-dimensional Euclidean space, there is exactly one sphere passing through four noncoplanar points. Four is the number of dimensions of space-time.

Words related to number four are indicated by the Greek prefix tetra (e.g., tetromino) or by the Latin prefix quadri- (e.g., quadrilateral). However, the prefix quadri- is also very commonly used to denote objects involving the number 2. This is the case because quadratum is the Latin word for square, and since the area of a square of side length x is given by x^2, a polynomial equation having exponent two is known as a quadratic ("square-like") equation. By extension, a quadratic surface is a second-order algebraic surface, and so on.

See also

Biquadratic Reciprocity Theorem, Burkhardt Quartic, Connect-Four, Diophantine Equation--4th Powers, Euler Quartic Conjecture, Four Coins Problem, Four-Color Theorem, Four Conics Theorem, Four-Dimensional Geometry, Four Exponentials Conjecture, Four Lemma, Four Travelers Problem, Four-Vector, Four-Vertex Theorem, Klein Quartic, Lagrange's Four-Square Theorem, Quadratic, Quadrilateral, Quartic Curve, Quartic Equation, Quartic Graph, Quartic Surface, Tetrahedron, Tetromino

Portions of this entry contributed by Margherita Barile

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Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, pp. 55-58, 1986.

Cite this as:

Barile, Margherita and Weisstein, Eric W. "4." From MathWorld--A Wolfram Web Resource.

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