Architecture and Geometry - A Very Old Marriage

Where Do We See Geometry in Architecture?

Vitruvian Man drawing by Leonardo Da Vinci (left) and Cesare Cesariano (right)
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 begins with geometry. Since earliest times, architects have relied on mathematical principles. The Greek mathematician Euclid of Alexandria is considered the first person to write down all the rules related to geometry, and that was way back in 300 BC. Then in about 20 BC the ancient Roman architect Marcus Vitruvius wrote down some rules about architecture in his famous De Architectura, or Ten Books on Architecture.


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It wasn't until centuries later, during the Renaissance, that interest in Vitruvius was reborn. Cesare Cesariano is said to have been the first architect to translate Vitruvius' work into Italian in about 1520. Decades earlier, however, the Italian Renaissance Man Leonardo da Vinci (1452-1519) sketched out the "Vitruvian Man" in his notebook, the iconic image imprinted onto our consciousness even today.

Models of Proportion:

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 Vitruvius recommended was 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.

Is Our Environment Shaped by Sacred Numbers and Hidden Codes?

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, including astrology, numerology, tarot, and feng shui, 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.

Absurd? Before you dismiss the idea of sacred geometry, take a few moments to reflect on the ways some numbers and patterns appear again and again in every part of your life. Patterns themselves may not be geometrically divine, or adhere to a mathematical ratio, but often they instill a sense of harmony in the observer.

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

Geometry in Your Garden
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.

Geometry in 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.

Geometry in 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.

Geometry in 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.

Geometry in 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.

Geometry and 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 suggest sacred shapes and ratios.

Geometry and 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. But why didn't he call the books The Vitruvius Code?

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. Moreover, 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.

Read & Do More:

  • The Return of Sacred Architecture: The Golden Ratio and the End of Modernism by Herbert Bangs, 2006
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  • Grids & Guides: 3 Notepads for Visual Thinkers, Princeton Architectural Press, 2015
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  • Architectural Geometry by Helmut Pottmann, Andreas Asperl, Michael Hofer, and Axel Kilian, Bentley Institute Press, 2007
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