As a matter of fact, geometry is the guiding principle of architecture. Marcus Vitruvius, an ancient Roman architect said that precise ratios must be used in construction. He said this based on his observation that the human body is modeled on precise ratio- the ratio of 1 to PHI (1.618). This ratio actually exists in every aspect of nature and is considered as the perfect ratio.

The pyramids themselves are a perfect example of the use of geometry in architecture. A cross section of a pyramid gives you a well defined triangle. This triangle, called the Egyptian triangle is based on specific ratios and proportions. While the importance of symmetry in architecture was greatly emphasized in the Renaissance periods, later centuries saw the development of the Cartesian planning. This is the term given to a grid plan which links architecture and geometry. Greek cities like Olynthus were designed on this kind of plan. Even modern cities are designed in the Cartesian plan. At the beginning of the twentieth century, Euclidean and Cartesian rectilinear geometry was widely used in architecture.

In this kind of architecture, one can see roof panes, balconies and wall panes which slide past or intersect each other. More recent kinds of architecture uses non-Euclidean geometry with non parallel walls and complicated 2 dimensional designs. This is not all. Even today, architects use a complex sketch of lines, triangles, circles and polygons calculated according to certain proportions to design a building. Corners, rooms, arches, windows, doors etc are designed on the basics of geometry. These days architects use computer graphics, computer aided design and other such software to integrate the basics of architecture and geometry.

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