Architectural Proportions 101

I joined Architecture school by accident. I wanted to become an engineer. Credit it to destiny or blame it on poor performance in chemistry; I landed up studying Architecture.  Someone told me it was a combination of arts, physics and mathematics, all three subjects I loved so I applied and got in. But then I had no clue about what to expect which was good, because I just enjoyed whatever came along. 

First year of Architecture was all about basic design. I enjoyed design studios. We could roam around, go grab a ‘cuppa’ and play music while designing. Coming from a straight-jacketed school, this freedom was exhilarating for me. We were encouraged to imagine the ‘unimaginable’ in basic design class and put it on paper. Since this was a ‘basic’ design class they wanted us to explore our design potential without getting bogged down by construction constraints although a lot of emphasis was on spatial quality and proportions.

I remember a design where we were given a cube of 3 x 3 x 3 meters and asked to create a community housing using only this cube. We spent hours playing with these cubes at 1:100 scale, creating living rooms, bedrooms, terraces and playgrounds. I remember this project vividly because that one cube and its repetition kind of lodged a sense of proportion in my mind.  We started with a single cube and then added, subtracted, multiplied, divided to create harmony in design.

  

Then sometime later I read about harmony in nature and how ancient architects used these principles to create buildings. Repetition of elements was done in a particular sequence to create balance in geometry. It was done in such a way that the part and the whole had similar geometry just like the microcosm of the macrocosm. Here’s an example how this principle exists in nature and its application in architecture.

Romanesco Broccoli
Logarithmic Fractal Design

In Romanesco broccoli each bud is composed of a series of smaller buds, an exact miniature copy of the larger. In short, each part is the same as the whole. 

Interesting similarity is seen in Indian temple architecture too. In Virupaksha temple at Hampi, Southern India, the temple 'Shikhara' has a fractal like structure where the parts resemble the whole.  The beauty of this design is that one can enjoy it from any distance. 

Virupaksha Temple at Hampi, Southern India

The repetition of elements in nature has a mathematical base. It follows Fibonacci sequence. The sequence is like 0,1,1,2,3,5,8, 13, 21…..so on and so forth. Each number is the sum of the earlier two numbers in the series. Everything in nature is governed by this sequence. Some common examples are flowers, pine cones, pineapples etc. Flowers have 2, 3, 5, 8 or even 21 petals. Pineapple scales are in Fibonacci sequence of 5, 8, 13.

How does this relate to architecture?

If you plot Fibonacci series in one line then it would look like this.

Now if you look at the Parthenon, built in 438 BC in Greece, our scale fits onto these proportions like a glove. The heights and the width are in perfect Fibonacci sequence.

Interesting fact about the Fibonacci series is the ratio one gets by dividing any number with the earlier number in the series. The ratio at first starts with 1/0=0, 2/1=2, 3/2=1.5….and settles to 8/5=1.6 and as the numbers progress to 1.618.

This number is called the 'Golden Ratio' or 'Phi' or better still, the 'Divine Proportion.' 

The Greeks developed a rectangle based on this proportion and called it the Golden Rectangle.

The Parthenon 

The Parthenon uses many such golden rectangles to break down its structural geometry into perfect harmony. 

This Proportion has always existed in the physical universe. It was discovered and rediscovered by physicist, artists and architects again and again over centuries. That explains different names given to this proportion. 

From the Golden Rectangle to ‘Form, Space, and Order’ and everything in between and beyond is about proportions. Ever wondered why some buildings appeal to us while some don’t? Why some architects have got it right and some haven’t? We’ll take a look at that in a later post. 

Until then look around and find the Fibonacci sequence around you. And just as Michael Schneider said in his interview, you can use this knowledge to your advantage in many ways. You have to know which flower falls into which number of Fibonacci series before you start plucking petals to ensure that she loves you always.

Bibliography

http://io9.com/5768696/the-fibonacci-series-when-math-turns-golden

http://www.goldennumber.net/golden-ratio-history/
http://www.keplersdiscovery.com/Proportion.html