Tuesday, October 15, 2013

The Golden Mean and Modern Design

This is one of my most popular blog posts of all time.  I thought that I would republish it.  It is fun to re-read!

I was first introduced to the Golden Mean in an Elements of Design class. My professor, in her French accent, sat at the front of the class and slowly and methodically explained the Golden Mean and how it relates to many things in the world; architecture, art, music, design. It was fascinating to me then and still is today.

The Fibonacci Sequence

1 2 3 5 8 13 21 34 55 89
Every figure is the sum of the two preceding
1 2 + 3 = 5 8 13 + 21 = 34 55 89

O.K. Stay with me here… The Golden Section is devised from this ratio. When a Golden Rectangle is progressively subdivided into smaller and smaller Golden Rectangles, a pattern is obtained. From this, a spiral can be drawn which grows logarithmically, where the radius of the spiral, at any given point, is the length of the corresponding square to a Golden Rectangle.

The given symbol of Phi, which symbolizes the Golden Ratio

Since then, it’s opened up a lot of doors for me in how I look at design, how I look at architecture and how balance and harmony are present in the world.

Since the Renaissance it has been used extensively in art and architecture, it has been used in historical and important architectures, such as the St. Mark's Basilica and the Parthenon and has become a standard proportion for width in relation to height as used in facades of buildings, in window sizing, in first story to second story proportion, even in the dimensions of paintings and picture frames.

The Parthenon in Athens, Greece

Ceiling Mosaic in St. Marks Basilica

Great Mosque of Kairouan

A geometrical analysis of the Great Mosque of Kairouan reveals a consistent application of the golden ratio throughout the design.

The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series.


Le Corbusier’s Villa Savoye, Poissy, France


Villa Savoye Plan View and the use of the GOLDEN SECTION (1:1.618).

Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's "Vitruvian Man", the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit.

Le Corbusier’s Modulor System

Le Corbusier took Leonardo's suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system.

File:Da Vinci Vitruve Luc Viatour.jpg

Leonardo da Vinci's Vitruvian Man (ca. 1487)


Palladio’s Villa Rotunda

The Villa Rotonda is symmetrical on all axes, including diagonals. Any architect will tell you this is hard to do, much less sell to a client; even Palladio only did it once, probably just to see if he could. Palladio based his design on simple progressions in the Fibonacci series leading to the Golden Mean. This is also hard to do.

In India, the Golden Mean was used in the construction of the Taj Mahal,
which was completed in 1648.

Piet Mondrian used the golden section extensively in his geometrical paintings

And today, architects are still frequently using the Golden Mean or Ratio in their work…

The CN Tower in Toronto, the tallest tower and freestanding structure in the world, has contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of Phi!

The College of Engineering at the California Polytechnic State University has a new Engineering Plaza based on the Fibonacci numbers.

What can you create using Fibonacci’s Golden Mean?


Things That Inspire said...

This is my kind of post!

I recently took a calligraphy class. I have always enjoyed doing calligraphy informally (on wedding invitations and such), and admire the form so much. What I learned in the class is how critical proportion is to beautiful calligraphy...and yes, calligraphers are well aware of the importance of the golden mean to achieving the correct proportion and scale in creating the letters.

It is really SO amazing! I also remember reading that Seurat used the golden mean when constructing some of his paintings.

citysage said...

LOVE this round up. What a busy blogger you have been while I was taking my self-enforced break! I remember being both utterly fascinated and completely confused with the golden mean during my short stint at design school. But anything to do with Le Corbu makes me happy!

Glenn Waggner said...

I had forgotten all about this. It makes me want to look at my paintings and see if they follow this formula. In other words, has the composition followed the formula intuitively, or was it learned and incorporated without realizing it?

Cote de Texas said...

Glenn is right - I wonder about that too - it might be instinctive when designing - pleasing to the eye in a way you can describe.

wonderful post! fabulous!

Laura Casey Interiors said...

Great post- just how I like to think and I love that you linked it all together.

Dmytro said...

Are there any actual proofs about Golden mean in Taj Mahal and Parthenon? If yes, what's your source?

Moessy said...
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Dmytro said...

You may be interested in exact information on this your interesting article topic here http://archgeom.blogspot.com/2010/03/golden-section-in-taj-mahal.html

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