Architecture is Awesome #17: The Golden Ratio

The Parthenon 

This is another in my series of posts inspired by 1000 Awesome Things, the Webby Award winning blog written by Neil Pasricha. The series is my meditation on the awesome reasons why I was and continue to be attracted to the art of architecture. 

Throughout history, whether knowingly or not, many architects have assigned aesthetically pleasing mathematical proportions to the buildings they designed that come close to what is widely known as the “Golden Ratio.” The approximate value of the Golden Ratio is 1 to 1.618. It is an irrational number often symbolized by the Greek letter “phi” ( Φ, φ ) and can be expressed by this formula: 

It was Euclid who, more than two thousand years ago, first identified the peculiar properties of the Golden Ratio (also referred to as the “Golden Section,” the “Golden Mean,” or the “Divine Proportion”). Many since Euclid have observed that people find both natural and manmade objects displaying dimensional relationships consistent with Golden Ratio to be well-proportioned, and thus most attractive. The ideal ratio is a match of the proportion between the parts and the parts to the whole. 

The Golden Ratio is closely related to the Fibonacci Sequence, which is a recursive formula wherein each successive generation of numbers is defined in terms of the previous two generations. The proportions of consecutive generations increasingly approach a fixed limiting value of 1.6180339887 . . . the Golden Ratio. 

The ratio is often expressed graphically and mathematically as a visually satisfying rectangle that can be split into a square and a smaller rectangle possessing the same aspect ratio as the rectangle it was cut away from. Infinitely repeating this process results in recursive generation of self-similar rectangles all displaying identical proportions. 

This Wikipedia and Wikimedia Commons image is from the user Chris 73 and is freely available at //commons.wikimedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg under the creative commons cc-by-sa 3.0 license 

The fact we find the proportion so frequently in the natural world at all scales (from the subatomic to the cosmic) is positively mind-blowing. We can see it in the pattern of seeds in the head of a sunflower, the spiraling chambers of a nautilus shell, and the formations of hurricanes and galaxies. Some claim our conceptions of human beauty are founded upon the natural occurrences of symmetries and the Golden Ratio in the dimensional relationships between one’s eyes, nose, mouth, etc. We may be primed to like physical characteristics that adhere to the Golden Ratio because it serves as a marker of reproductive fitness and health. 

The west facade of the Cathedral of Notre Dame in Paris exhibits proportioning in accordance with the Golden Mean (photo by Peter Haas CC BY-SA 3.0 licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license).

Many famous works of architecture clearly exhibit compositions utilizing approximations of the Golden Ratio in plan, section, and elevation. The Parthenon is an oft-cited (if imperfect) example. So too are many of the works of the Renaissance architect Leon Battista Alberti and his contemporaries. Le Corbusier based his Modulor proportional system upon the Golden Ratio, the 1927 Villa Stein and his later Unite’ d’habitation projects perhaps being among the most notable and obvious examples of its application. 

Le Corbusier's Modulor inscribed on the wall of the Unite’ d’habitation in Berlin (photo by Jean-Pierre Dalbéra from Paris, France (Corbusierhaus (Berlin)) [CC BY 2.0  (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons) 

The physicist Max Tegmark posits we live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from the numerical bonds between them. He says our physical world is effectively one giant mathematical object. It is the relationship between numbers—especially seemingly magical ones like the Golden Ratio—and the nature of reality that has fascinated and inspired architects ever since the time of the Ancient Greeks. 

Growing up, dealing with numbers was never my strong suit. I was a middling student at best when it came to math; nevertheless, the idea that everything in our existence is somehow mathematical fascinates me today. As an architect I try to make sense of what it all means to the work I’m engaged in. Like Max Tegmark, I’m convinced there’s more to it all, something undeniably extraordinary and useful to the design of our built world. At the most essential level, proportional systems like the Golden Ratio hint at the astonishing, amazing, and AWESOME beauty inherent in our mathematical universe. 

Next Architecture is Awesome: #18 Evanescent Ruins