Before I start, let’s see this beautiful video “Nature by Numbers” by Cristóbal Vila. I first saw this almost 9 years back and it helped discover a lot of amazing knowledge treasures which I didn’t know before. This number is used by architects and designers extensively, but what we are discussing here is something else. It’s about realizing and pondering on how the entire universe is crafted specifically in a specific metric. Have a look at the video and I shall elaborate further with detailed illustrations. I was pretty pumped up when I first came to know about this and would like to take this write up as an opportunity to share this information with you. Probably this would be the first write up for which I spent the longest time preparing content and illustrations for the only reason that I’m super excited to share this all of you. Now, let’s read.
This piece would be an addition to the Ponder Series that we have been writing extensively over the past several months. When we think about the world around us and also when we look within, it might seem usual and ordinary. But ponder series, as you might know, is all about thinking deeply and delving into the details by going beyond the ordinary perceptions. “Golden Ratio” is such a concept that’ll blow our minds off. I first read about this interesting ratio pervading the universe when I was in college. I shall elucidate it here, preferably with some visual illustrations. If you have not heard about this before, I’m sure this will definitely throw you into some wonder. Read it very carefully. It’s exciting information!
Many of us would be familiar with the Fibonacci series of numbers which were discovered by the Italian mathematician Leonardo Fibonacci in 1202 B.C.
It’s a series as below:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, …
In this series, if you add two numbers in the series, you’ll get the next number in the series. For example, 0+1=1, the third number in the series. And 1+1=2, the fourth number in the series, 1+2=3, the fifth number in the series and so on.
We might have seen this series in our maths classes and wondered what is special about them. They have an amazing property. If we divide any number in this sequence by the number before it, we would get numbers very close to each other. After the 13th number in this series, the ratio is constant and we get 1.618. This is called “Golden Ratio”
233 / 144 = 1.618
377 / 233 = 1.618
610 / 377 = 1.618
987 / 610 = 1.618
1597 / 987 = 1.618
2584 / 1597 = 1.618
Now, this golden ratio number of 1.618 is pervading everywhere. If you didn’t know this before, get prepared to be blown away.
Human Body
Did we ever think that our body measurements were just random? Boy! we are wrong! The proportions and geometrical ratios are carefully crafted in this specific ratio. For a better visual perspective, I’m sharing a few illustrations below so that you can take a look! These values are universally true for every human body. Isn’t that a jaw-dropping realization if you didn’t know this before?
– Length of face/width of the face,
– Distance between the lips and where the eyebrows meet / length of the nose,
– Length of face/distance between the tip of the jaw and where the eyebrows meet,
– Length of mouth/width of the nose,
– Width of nose/distance between nostrils,
– Distance between pupils/distance between eyebrows.
Even the placement of teeth, as well as the ratio of individual teeth sizes, are on this same ratio.
In a research study carried out in 1987, it was discovered that this magic ratio is also in the structure of the lungs as well. The bronchi network in the lung is asymmetric. The windpipe gets divided into the left and the right bronchi networks. The one on the right is short and the one on the left is long. The geometrical proportion of the shorter one to the longer one of this bronchi is 1.618. Isn’t that amazing? Recent studies have shown that the internal structures of the ears are also proportioned in the same ratio. The more we explore and delve in, the more breathtaking it turns out to be.
This number has garnered significant interest in great minds like Pythagaurus, Leonardo Da Vinci and the famous astronomer Kepler. Leonardo Da Vinci has used it in the painting Monalisa.
Golden Ratio in DNA Helix
DNA has two grooves in its spiral. Major to minor groove proportion measures as the golden ratio 1.618.
Golden Spiral
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. See the below link for a reference.
Image By Jahobr – CC0, Link
The golden spiral can be found in pinecones, sunflowers, pineapples, and a lot of other plants. Another amazing detail is that the petals of plants commonly grow in Fibonacci numbers.
In sunflower, we can notice two families of spiral patterns: one winding clockwise and the other counterclockwise. The quantity of spirals in each family are always two consecutive Fibonacci numbers. This effect is the result of closely packing points separated by 137.5 degrees in tight spirals. This implies that the a golden-ratio based phyllotaxis allows not only for optimal sun exposure but also for maximal packing in horizontal space. (Reference)
For field daisies, the count of petals is usually either thirteen, twenty-one, or thirty-four petals, all consecutive Fibonacci numbers. Bet you didn’t know about this before! 🙂
And it’s not over yet. We have more!
The golden ratio is even found in the shape of galaxies, hurricanes, and waves.
What I have shown here is only a small portion or subset of how this golden ratio pervades in almost every other stuff we are surrounded with. Leonardi Davinci has used this ratio in some of his greatest paintings. Architects use this ratio in designing structural solutions with better aesthetics. In architecture, they bring balance and height to structures and allow the usage of specific geometries and varying shapes and eventually help build aesthetic structures. They are also extensively used in arts and music as well. The ratio is made use of in the design of several musical instruments and in timing musical compositions (Climax reaching at 61.8% of the song sequence to make it more appealing, for instance). Beethoven’s fifth symphony uses this ratio. The ratio is also used in other fields like facial plastic surgery and cosmetic dentistry. This is really thought-provoking. If we ponder deeply on these realities, we come to the realization that everything around us is formed and ordered in a measure which we even don’t notice. We require the eye of wisdom and insight to contemplate these realities. Don’t let these astonishing marvels around you hide from your thoughts and cogitations when we get engulfed ourselves in the blurred rush of routine life. Uncovering this hidden mathematical miracle around us has a profound impact. Think about it, friends! Let’s widen our horizons and augment our perspectives. Personally, I believe this ratio is sort of like a divine signature. God bless friends!
I appreciate the research done by the author for this study & you have nicely presented it as well. Since I spend my valuable time reading through it, I would like to mention several points even-though you may find contradictory to your findings.
In my opinion, the golden ratio’s aesthetic importance is actually an urban legend or a design unicorn rather than a precisely proven scientific entity. Many designers don’t use it and if they use it, more often than not, they use it involuntarily. There is no science to precisely back it up. Whoever believing that this golden ratio is the hidden math behind the beauty in humans, nature & for that matter universe are falling for a myth.
Let’s speak about this mathematically, Since the golden ratio is an irrational number, it is impossible for anything in the real world to fall into the golden ratio. All the examples that you ave researched are simply floating around it. The golden ratio is like “pi”; just as it is impossible to find a perfect circle in the real world, the golden ratio cannot strictly be applied to any real worlds object. It is always going to be a little here or there.
If we are speaking about human body, it is a very complex structure & it is very easy to come up with examples of ratios that are close to 1.6. Recently we hear about numerous studies conducted by Golden-Ratio-backed-beauty enthusiasts analyzing some of the popular actress’s face ratios & debating which one come close to the Golden Ratio. I am sure none of them will be 100%.
The spiral of the Nautilus shell doesn’t fit precisely within a golden ratio. Each Nautilus shell does maintain the same proportion through out the animal’s life but that is a logarithmic spiral & that proportion is not generally in the precise golden ratio.
Now we come to the art. The use of proportions when drawing human body is nothing new. In fact Da Vinci studied this proportions & came up with 15 rules of proportions in his “Vitruvian Man”. Leonardo Da Vinci’s collaboration with Luca Pacioli, the author of Divina Proportione, have led some to speculate that he incorporated the golden ratio in his Vitruvian Man but it is not supported by any of his writings & the proportions in Vitruvian Man do not match Golden Ratio precisely.
Also, Marcus Vitruvius Pollio (80-15BC), commonly known as the the world’s first known engineer (if you are discounting the ancient engineer Vishwakarma, who invented Pushpaka Vimana, of course), wrote his works on architecture in 25BC & he stated that human body & perfect building are similar. Phidias (in commemoration of whom Mark Barr coined the term “phi” to reflect the idea of Golden Ratio) was a Greek sculptor who sculptured Zeus at the Temple of Olympia, one of the 7 wonders of the ancient world. He was known to use some ratio similar to the Golden Ratio(I said similar, not precise) & the Golden Ratio was termed Mean of Phidias. All these little tips of details from the ancient books created a spark in those people, who are just as adventurous as the Spanish conquistadors who searched & searched for El Dorado in vain, & they created this myth of Golden Ratio. If someone asks me whether the unicorn is real, my answer will be a straight NO; just like if you ask me whether I believe that the Golden Ratio is a precise universal phenomena behind it’s beauty or arrangement.
Mankind is always susceptible to myths & coloured stories that provide more fiction than facts. Look at the degree of popularity achieved by Dan Brown’s Da Vinci Code, for example. It doesn’t surprise me that some people are blown away by such ‘so called’ revelations.
Thank you MHP.