How Is Geometry Important to Architecture?

Geometry and Design

• A building, whether it is a home or a skyscraper, can be thought of as a series of interrelated structural elements designed on geometrical principles. Lines and shapes are designed to work together to create structural integrity in specific applications. For example, the roof of a house in an area prone to heavy snowfall will be a triangle with steeper sides to allow snow to fall off, while a flat roof would be more suitable in a dry, warm climate.

Geometry and Framing

• Geometric calculations are also used to ensure safety in the framing of a structure. In a large steel-framed building, for example, calculations are made to determine the weight load on the base of the building, and grid made up of smaller rectangles is used to distribute weight evenly to ensure the building's structural integrity. Even in residential framing, geometric calculations are used to determine load-bearing elements like floor joists and beams and practical concerns like roof pitch.

Geometry and Aesthetics

• In addition to structural considerations in architectural design, geometry is also used to improve the aesthetic appeal of a building. Whether it is through a series of related rooflines to create a dynamic façade or through the use of oval spaces to create interesting internal spaces (as was common in Baroque architecture), architects have always attempted to use geometrical principles to make buildings more attractive. At times, these designs are closely related to structural necessities, as in the use of flying buttresses in Gothic architecture.

The Golden Ratio

• One geometrical concept that has been historically incorporated into architectural design is the "Golden Ratio," or Phi. This ratio, expressed as the number 1.618, is utilized in shapes that are thought to be the most aesthetically pleasing, the "Golden Rectangle" and "Golden Triangle." These shapes are present in many historical structures, including the Great Pyramid of Giza and the Parthenon. Because of this ratio's presence in both nature and art, it continues to be of interest to both mathematicians and architects.