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 is given by , 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.