How to Use Geometry in Architecture

Geometry is the area of mathematics that is basically the analyses and measurements of shapes and their properties.  Together with physics, geometry is integral to architecture's designs from the first lines on the drafting board to the final landscaping around a finished building.  Geometry also is concerned with symmetry and economy of line; these form the bridge of sciences to the arts of architecture.

Locating Geometry in Architecture

• Angles, distances and space measurements in geometry form the first shapes of a design on the architect’s first draft.


• As an architect changes angles and twists them, he must consider the changes this makes in the volume of the rooms and subsequent losses or gains throughout the structure.


• Geometry calculates the changes in ratios of horizontal and vertical surfaces as a design is worked and reworked.

How Geometry is Used

• Geometric calculations tell the architect whether or not he has enough volume in his form for all the special requirements of the functional elements that must be included in the structure.


• As usually form must follow function, he can then make whatever changes bring these into alignment.


• An architect has been trained in shapes and knows what shapes give a structure strength more than others; this knowledge learned from the geometry in an architect’s training is why an architect will choose a particular size of a shape and have it made of particular materials.

The Golden Rule

• One of the cardinal rules of geometry is the golden rule.  


• The golden rule is also known as the divine proportion and is part of the area of sacred geometries.  


• Simply put, the golden rule says to achieve the most pleasing and beautiful of designs the forms and shapes within the design should be of a ratio of one to three.  An example of this in architecture is the building in the form of a triangle known as the Flatiron Building in Chicago which was designed by Stieglitz.

Energy Efficient

• Geometry can tell the architect how energy-efficient his design is.  


• Volume and surface area ratios form a proportion that gives the amount of heat loss that can be expected in a structure.  Added into this equation are the shapes and volume of any windows and doors that are in the structure and their placement facing the sun during the day.  


• Heat or air conditioning loss through walls and window openings with more fragile weather shielding can tell whether or not the building needs more R-factor in the roofing or insulation in the attic to make up for having more than a usual amount of window frontage to a southern or northern exposure.  


• These kinds of calculations advise the architect how and when to make up for the amount of load on the building’s heating and cooling system and still remain in qualification as an energy-efficient structure.