Symmetry and Proportion in Design

Architecture depends on symmetry, what Vitruvius calls the "proper agreement between the members of the work itself." Symmetry is from the Greek word symmetros meaning "measured together." Proportion is from the Latin word proportio meaning "for the part," or the relationship of the portions. What humans consider "beautiful" has been examined for thousands of years.

Humans may have an innate preference for what looks acceptable and beautiful. A man with tiny hands and a large head may look out of proportion. A woman with one breast or one leg may look asymmetrical. Humans spend an enormous amount of money every day on what they consider is a beautiful body image. Symmetry and proportion may be as much a part of us as our DNA.

How do you design and build the perfect building? Like the human body, structures have parts, and in architecture those parts can be put together in many ways. Design, from the Latin word designare meaning "to mark out," is the overall process, but design outcomes depend on symmetry and proportion. Says who? Vitruvius.

De Architectura

Ancient Roman architect Marcus Vitruvius Pollio wrote the first architecture textbook called On Architecture (De Architectura). Nobody knows when it was written, but it reflects the dawn of human civilization — in the first century B.C. into the first decade A.D. It wasn't until the Renaissance, however, when the ideas of ancient Greece and Rome were reawakened, that De Architectura was translated into Italian, French, Spanish, and English. During the 1400s, 1500s, and 1600s, what became known as The Ten Books on Architecture was widely distributed with a number of added illustrations. Much of the theory and construction basics spelled out by Vitruvius for his patron, the Roman Emperor, inspired Renaissance architects and designers of that day and even those in the 21st century.

So, what does Vitruvius say?

Leonardo da Vinci Sketches Vitruvius

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Architecture, Geometry, and the Vitruvian Man

By Jackie Craven

Leonardo da Vinci (1452–1519) is sure to have read Vitruvius. We know this because da Vinci's notebooks are filled with sketches based on the words in De Architectura. Da Vinci's famous drawing of The Vitruvian Man is a sketch directly from the words of Vitruvius. These are some of the words Vitruvius uses in his book:

SYMMETRY

• in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle
• And just as the human body yields a circular outline, so too a square figure may be found from it.
• For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.

Note that Vitruvius begins with a focal point, the navel, and the elements are measured from that point, forming the geometry of circles and squares. Even today's architects design this way.

PROPORTION

Da Vinci's notebooks also show sketches of body proportions. These are some of the words Vitruvius uses to show relationships between elements of a human body:

• the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height
• the open hand from the wrist to the tip of the middle finger is a tenth part of the whole body
• the head from the chin to the crown is an eighth part
• with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth
• from the middle of the breast to the summit of the crown is a fourth
• the distance from the bottom of the chin to the under side of the nostrils is one third of it
• the nose from the under side of the nostrils to a line between the eyebrows is a third
• the forehead, from between the eyebrows to the lowest roots of the hair, is a third
• the length of the foot is one sixth of the height of the body
• the length of the forearm is one fourth the height of the body
• the breadth of the breast is also one fourth the height of the body

Da Vinci saw that these relationships between elements were also the mathematical relationships found in other parts of nature. What we think of as the hidden codes in architecture, Leonardo da Vinci saw as divine. If God designed with these ratios when He made man, then man should design the built environment with the ratios of sacred geometry. "Thus in the human body there is a kind of symmetrical harmony between forearm, foot, palm, finger, and other small parts," writes Vitruvius, "and so it is with perfect buildings."

Designing with Symmetry and Proportion

Although European in origin, the concepts written down by Vitruvius seem to be universal. For example, researchers estimate that Native American Indians migrated to North America from Northern Asia about 15,000 years ago — well before even Vitruvius was alive. Yet when European explorers like Francisco Vásquez de Coronado from Spain first encountered the Wichita people in North America in the 1500s, symmetrical huts of grass were well-built and proportioned large enough to house entire familes. How did the Wichita people come up with this conical design and the proper agreement described by the Roman Vitruvius?

Concepts of symmetry and proportion can be used purposefully. Modernists of the early 20th century defied Classical symmetry by designing asymmetrical structures. Proportion has been used in spiritual architecture to accentuate the holy. For example, the Po Lin Monastery in Hong Kong shows not only the symmetry of the San Men Chinese mountain gate, but also how proportion can bring attention to the outlandishly large Buddha statue.

By examining the human body, both Vitruvius and da Vinci understood the importance of "symmetrical proportions" in design. As Vitruvius writes, "in perfect buildings the different members must be in exact symmetrical relations to the whole general scheme." This is the same theory behind architectural design today. Our intrinsic sense of what we consider beautiful may come from symmetry and proportion.

Sources

• Vitruvius. "On Symmetry: In Temples and in the Human Body," Book III, Chapter One, Ten Books on Architecture translated by Morris Hicky Morgan, 1914, The Project Gutenberg, http://www.gutenberg.org/files/20239/20239-h/20239-h.htm
• Raghavan et al. "Genomic evidence for the Pleistocene and recent population history of Native Americans," Science, Vol. 349, Issue 6250, August 21, 2015, http://science.sciencemag.org/content/349/6250/aab3884
• "Wichita Indian grass house," Kansas Historical Society, http://www.kansasmemory.org/item/210708