The Perfect Square

In the Oxford English Dictionary, the square is described as an equilateral rectangle, that is, a plane figure with four equal sides and four right angles. The square is an irreducible figure, one of the few in nature. There are no subdivisions in a square, only other, smaller squares. A figure is either a square, or it is not. QED.
The word square has entered our language to describe an entity or person that is solid, reliable, dependable, unmistakeable, e.g., a square meal, or a fair and square deal. But it has darker connotations. If a subject embraces definite, usually conservative, political views, or adheres to a certain mode of life, resisting all forces of change, we often describe him as square. Depending on your point of view, being square may or may not be a good thing. The square, born of Euclidean geometry, is almost always a human construct and almost never occurs in the natural world. Instead, we see it in architecture, in town planning, and it is used exclusively to construct the Platonic world of the chessboard. It is often used to represent the ideal, the unattainable, it being no accident that the mortarboard of the academic is square.