Architecture and Math: A Perfect Ratio

When I went on a family trip to the Math Museum in Manhattan, I was delighted to see children creating artful buildings with blocks, using computers to make their own fractals, and—the real highlight—riding bicycles on square wheels along a rounded track. Over the years, many people have asked me about the importance of math in architecture. Calculations are essential to determining the structural and mechanical aspects of a building, but math also provides a crucial humanistic component to architectural design.

A golden section diagram of Palladio’s Villa Rotunda.

Math is at the basis of proportion and visual order in buildings all around the world. My work at I.M. Pei introduced me to design based on squares and triangles. Another fascinating mathematical relationship occurs in Japanese architecture, with a link between architectural units and the proportions of the human body. A tatami mat is designed to fit two people sitting or one person sleeping. Room sizes in Japan are often determined by the number of tatami mats that fill the space.

During the Renaissance, architects believed that there were ideal proportions essential to achieving architectural harmony. Palladio used systems of circles, squares, and double squares in his designs, and derived an ideal mathematical proportion known as the Golden Section, or the Golden Ratio. Le Corbusier turned to this proportion in designing Villa Stein, the famed home of Gertrude Stein’s brother. I had an exciting opportunity to design an Italian villa in Northern New Jersey, inspired by the clients’ knowledge of Roman architecture and proportion. The owner wrote to me recently that when visiting the house, “people seem to be especially relaxed and at ease. I wonder if it has to do with the fact that the building was designed on a four-foot grid.” There does seem to be an inherent harmony when mathematical principles underlie the design plan.