Definition:Square

Algebra
Let $$n$$ be a number.

Then the square of $$n$$ is $$n \times n$$ and can be written $$n^2$$.

Abstract Algebra
Let $$\left({S, \circ}\right)$$ be an algebraic structure.

Let $$x \in S$$.

Then the square of $$x$$ is $$x \circ x$$ and can be written $$x^2$$.

Geometry
In geometry, a square is a four-sided plane figure in which all of the angles are right angles and all of the sides are the same length.

A geometric square has an area of $$L^2$$ where $$L$$ is the length of a side of the square.