Inhabiting the Square

Geometries and geometric systems are not architecture, though architecture is geometric. Geometries and geometric systems, because of their autonomous nature, are generally understandable and can serve as the basis of communicable patterns expressed in architectural form, even though they are not necessarily at the base of man's structural understanding of environmental order. As a method of illustration, this study focuses on the geometry of the square, realizing its persistent and valued use in architectural works of all peoples, in all cultures, throughout all of history. The square is considered as the basic geometric unit which generates the cube, the grid, and the frame. The square and its derivatives are examined with regard to their inherent quantitative, qualitative, and structural properties.