The Golden Ratio - Hidden Codes in Architecture

Mosaic Tile Forming a Fibonacci Type Spiral
Mosaic Tile Forming a Fibonacci Type Spiral. Photo by Cole Vineyard / E+ / Getty Images
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God's Specifications

Armrest of a wrought iron bench forms a Golden spiral of the Divine Ratio, a pleasing geometry
Armrest of a wrought iron bench forms a Golden spiral of the Divine Ratio, a pleasing geometry. Photo by Peter Tansley/Moment/Getty Images (cropped)

The Golden Ratio is a complicated mathematical theory said to be used by artists and architects for its natural beauty of proportion in design. "It's theory tells us," explains architect William J. Hirsch, Jr., "that human beings are most pleased when things are in a proportion of 1 to 1.618." The ratio can be visually produced. Compare the armrest of the bench in this photo with the graphical (mathematical) representation of the golden ratio spiral.

Ever since author Dan Brown published his best seller, The Da Vinci Code, the world has been intrigued with hidden codes, the mathematics of design, and Leonardo da Vinci's famous drawing, The Vitruvian Man. The archetypal man da Vinci drew became a symbol for concepts of "spiritual geometry" and classical theories of proportion and design.

God's Specs

The idea is that man's creations—buildings, sculptures, pyramids—can be consciously designed to God's mathematical specifications. What are God's specs? The Italian mathematician Fibonacci, who lived in a world of Christianity (1170-1250 AD), was one of the first to give numbers to God's organic creations.  Fibonacci observed that plants, animals, and humans were all built around the same mathematical ratio, and, because these "natural" objects were created by God, the proportions must be divine, or golden.

Fibonacci often gets the credit, but his calculations were built on the work of the Greek mathematician Euclid. It was Euclid who mathematically described relationships between line segments and documented the extreme and mean ratio. But his thirteen books, collectively called Elements, were written Before Christ (BC), so "divinity" had nothing to do with it.

Other Names for the Hidden Code

  • extreme and mean ratio
  • divine proportion or divine ratio
  • divine section (sectio divina)
  • golden ratio or golden spiral
  • golden section (sectio aurea) or golden proportion
  • golden mean or golden number
  • miraculous spiral (spira mirabilis)
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Plotting the Golden Mean - A Graphical Representation

Graphical representation of the golden ratio spiral
Graphical representation of the golden ratio spiral, a complicated mathematical theory said to be used by artists and architects for its natural beauty of proportion in design. Illustration art by John_ Woodcock/iStock Vectors/Getty Images

From the human face to the nautilus shell, the golden ratio was God's perfect design. Through complicated formulas and sequences of numbers, the most aesthetically pleasing, beautiful, and natural design has a ratio of 1 to 1.618, or 1 to the Greek letter φ (that's phi, not pi). The mathematics of proportion and the geometry of ratios were convincing architectural models to follow.

As Christianity dominated the Western Roman Empire in northern Italy, mathematicians of the Renaissance put a religious spin on the ratio. Leonardo da Vinci and others observed that this proportion seemed to be present not only in the human body, as Vitruvius said, but also in the design of many natural objects, like flower petals, pine cones, and nautilus shells. The ratio, found throughout God's creatures, was considered divine. In 1509, the Italian-born Luca Pacioli (1445–1517) wrote a book called De Divina Proportione or The Divine Proportion, and he asked Leonardo da Vinci to illustrate it.

Even when faced with evidence that the nautilus spiral is not part of the divine ratio, the belief persists.

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The Golden Ratio in Architecture - The Great Pyramids

The Pyramid of Khafre (Chephren) in Giza, Egypt
The Pyramid of Khafre (Chephren) in Giza, Egypt. Photo by by Lansbricae (Luis Leclere)/Moment/Getty Images (cropped)

Within the built environment, design can be artistic and intuitive based on observation, but also technical based on mathematics and engineering.

Paul Calter, author of Squaring the Circle, takes a mathematical approach in his course called Geometry in Art and Architecture at Dartmouth College. With a series of equations, Calter proves that the ratio of the slant height of the Pyramids of Giza (2000 BC) to half the pyramid's base is the same as the golden ratio, 1 to 1.618. The world's early structures may have followed the golden ratio design, but we don't know if it was on purpose.

Later designers, like Le Corbusier, did do it on purpose—intentionally creating architecture based on these proportions.

More Examples of the Golden Ratio in Architecture

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Brunelleschi's Dome in Florence

Brunelleschi's Dome (the Duomo) and the Bell Tower by night in Florence, Italy
Brunelleschi's Dome (the Duomo) and the Bell Tower by night in Florence, Italy. Photo by Hedda Gjerpen/E+/Getty Images (cropped)

By the time Leonardo da Vinci was born in 1452, Filippo Brunelleschi had already built the famous dome atop Santa Maria del Fiore in Florence, Italy. Some say that the engineering feat was accomplished with divine intervention; some say it was divine proportion. But whose name is more associated with ? Not Brunelleschi.

Leonardo was not the first to explore the mysteries of symmetry and proportion.  The Roman architect Vitruvius put mathematical theory into practice in 30 BC when he wrote De architectura, a work rediscovered in 1414 AD, the early Renaissance. Then there was the invention of the printing press in 1440, which made these ancient writings more widely available—even to Leonardo da Vinci. A return to these Classical ideas is what defines Renaissance Architecture.

Does the number 1.618 (Phi) define a universal design? Maybe. Today's architects and designers may unconsciously or purposely design by this aesthetic. Some say that even Apple Inc. used the ratio to design their iCloud icon.

So, when you look at the built environment, consider what appeals to your own sense of beauty; it may be divine or it may be just marketing.


  • Designing Your Perfect House: Lessons from an Architect by William J. Hirsch, Dalsimer Press, 2008, p. 52
  • Sea Shell Spirals by Ivars Peterson, Science News, April 1, 2005 [accessed June 15, 2014]
  • Photo of Villa Savoye by Esther Westerveld, westher on, Creative Commons, Attribution 2.0 Generic