Architecture, Geometry, and the Vitruvian Man

Where Do We See Geometry in Architecture?

Vitruvian Man drawing by Leonardo Da Vinci (left) and Cesare Cesariano (right)

Left image (crop) by Rob Atkins / Photographer's Choice / Getty Images; Right image by Philip and Elizabeth De Bay / Corbis Historical / Getty Images

Architecture could be said to begin with geometry. Since earliest times, builders relied on imitating natural forms—like the circular Stonehenge in Britain—and then applied mathematical principles to standardize and replicate the forms.

The Beginnings

The Greek mathematician Euclid of Alexandria is considered the first to write down all the rules related to geometry in 300 BCE. Later, in about 20 BCE, the ancient Roman architect Marcus Vitruvius penned more rules in his De Architectura, or Ten Books on Architecture. Vitruvius is responsible for all the geometry in today's built environment—at least he was the first to write down the proportions for how structures should be constructed.

Renaissance Popularity

It wasn't until centuries later, during the Renaissance, that interest in Vitruvius became popular. Cesare Cesariano (1475-1543) is considered the first architect to translate Vitruvius' work from Latin into Italian in about 1520 CE. Decades earlier, however, the Italian Renaissance artist and architect Leonardo da Vinci (1452-1519) sketched out the "Vitruvian Man" in his notebook, making da Vinci's the iconic image imprinted onto our consciousness.

The images of the Vitruvian Man are inspired by the works and writings of Vitruvius. The "man" portrayed represents the human being. The circles, squares, and ellipses that surround the figures are Vitruvian calculations of man's physical geometry. Vitruvius was the first to write his observations about the human body—that the symmetry of two eyes, two arms, two legs, and two breasts must be an inspiration of the gods.

Models of Proportion and Symmetry

Vitruvius believed that builders should always use precise ratios when constructing temples. "For without symmetry and proportion no temple can have a regular plan," Vitruvius wrote.

The symmetry and proportion in design that Vitruvius recommended in De Architectura were modeled after the human body. Vitruvius observed that all human beings are shaped according to a ratio that is astonishingly precise and uniform. For example, Vitruvius found that the human face equals one-tenth of the total body height. The foot equals one-sixth of the total body height. And so on.

Scientists and philosophers later discovered that the same ratio Vitruvius saw in the human body—1 to phi (Φ) or 1.618—exists in every part of nature, from swimming fish to swirling planets. Sometimes called a "golden ratio" or "divine ratio," the Vitruvian "divine proportion" has been called the building block of all life and the hidden code in architecture.

Geometry in Our Environment

"Sacred geometry," or "spiritual geometry," is the belief that numbers and patterns such as the divine ratio have sacred significance. Many mystical and spiritual practices begin with a fundamental belief in sacred geometry. Architects and designers may draw upon concepts of sacred geometry when they choose particular geometric forms to create pleasing, soul-satisfying spaces.

The following examples of geometry in the environment frequently influence architectural design.

The Body
When studied under the microscope, living cells reveal a highly ordered system of shapes and patterns. From the double helix shape of your DNA to the cornea of your eye, every part of your body follows the same predictable patterns.

Gardens
The jigsaw puzzle of life is made up of recurring shapes and numbers. Leaves, flowers, seeds, and other living things share the same spiral shapes. Pine cones and pineapples, in particular, are composed of mathematical spirals. Honeybees and other insects live structured lives that mimic these patterns. When we create a floral arrangement or walk through a labyrinth we celebrate nature’s innate forms.

Stones
Nature’s archetypes are reflected in the crystalline forms of gems and stones. Amazingly, the patterns found in your diamond engagement ring may resemble the formation of snowflakes and the shape of your own cells. The practice of stacking stones is a primitive, spiritual activity.

The Sea
Similar shapes and numbers are found beneath the sea, from the swirl of a nautilus shell to the movement of the tides. Surface waves themselves are patterned, like waves that pulse through air. Waves have mathematical properties all their own.

The Heavens
Nature’s patterns are echoed in the movement of planets and stars and the cycles of the moon. Perhaps this is why astrology lies at the heart of so many spiritual beliefs.

Music
The vibrations we call sound follow sacred, archetypal patterns. For this reason, you may find that certain sound sequences can stimulate the intellect, inspire creativity, and evoke a deep sense of joy.

The Cosmic Grid
Stonehenge, megalithic tombs, and other ancient sites stretch across the globe along underground electromagnetic tracks or ley lines. The energy grid formed by these lines suggests sacred shapes and ratios.

Theology
Best-selling author Dan Brown has made a lot of money by using the concepts of sacred geometry to weave a spell-binding tale about conspiracy and early Christianity. Brown's books are pure fiction and have been hotly criticized. But even when we dismiss The Da Vinci Code as a tall tale, we can't dismiss the importance of numbers and symbols in religious faith. Concepts of sacred geometry are expressed in the beliefs of Christians, Jews, Hindus, Muslims, and other formal religions.

Geometry and Architecture

From the pyramids in Egypt to the new World Trade Center tower in New York City, great architecture uses the same essential building blocks as your body and all living things. In addition, the principles of geometry are not confined to great temples and monuments. Geometry shapes all buildings, no matter how humble. Believers say that when we recognize geometric principles and build upon them, we create dwellings that comfort and inspire. Perhaps this is the idea behind the architect's conscious use of divine proportion like Le Corbusier did for the United Nations building.