The smallest positive composite number and the first evenperfect 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 onesphere 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.