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Math of Beauty, how Math explains beauty

November 1st, 2008

People care about beauty. In fact, they care a lot. But while everyone wants to be beautiful, they had stopped asking what beauty really is. It was not always this way.

In ancient Greece, scholars were convinced that the definition of beauty is concrete and mathematical. Pythagoras, an early thinker, had impressive answers. He showed that the notes of music were not arbitrary but it reflects the notes of strings when its length is subdivided into the ratio of 2:1 or 3:2. And in design and architecture, he managed to show that the shapes and structures people found most attractive contains the “golden ratio”.

So what exactly is the “golden ratio”? Well, it is primarily based on the Fibonacci numbers wherein every number in the sequence is the sum of the previous two numbers. The Fibonacci sequence is as such:

1, 1, 2, 3, 5, 8, 13, 21… and this can lead to the Golden ratio of 1.61

Very little progress has been made since then until Leonardo da Vinci drew a sepia sketch of the Vitruvian Man. It is the famous sketch of a nude and spread-eagled man touching a circle and square with his extremities. The sketch asserts an uncanny proportional coincidences of what the ideal human form should look like (arm span = height, height = hand length X 10). But this proportion did not delve into the face.

Dr. Stephen Marquardt, a plastic surgeon based on Southern California, decided to go at it alone. His patients weren’t from beautiful girls or divorcees who want to augment their features with a small surgery here and there. People who come to him are deformed. They don’t want chin augmentation, they simply want a chin and they left it up to the doctor to decide which size would be right for them.

Here is the paradox. The fact that his patient’s weren’t concerned about aesthetic perfection meant that the doctor had to think about it at all times. It is more difficult than it sounds because a seemingly perfect chin might not work on the face on the aesthetic level. He collected the photographs of the most beautiful faces in the world and measured its dimensions.

Something exhilarating began to present itself: the golden ratio. Beautiful faces had mouths that were 1.618 times wider than their nose and their nose are 1.618 times wider than the tips of the nose. And the triangle forced by the nose to the mouth is the perfect acute triangle.

Is beauty in the eye of the beholder? Some would think so but no one can deny that the golden ratio does play a role in that perception.

  1. November 4th, 2009 at 18:35 | #1

    I made a large paper on Stephen Marquardt. I agree on everything you say but I must say that Marquardt did not discover anything. He uses the golden ratio on his work but what he proposed, the so called beauty mask, is a tool barely based on a rigurous method. It works exactly the same as if a photograph or an impression of a caucasian model were used.

    The golden ratio has been used in odontology and other medical branches in relation to the human face long before marquardt.

    What you mention about if beauty really relies in the eye of the beholder is something i ask myself everyday and i am convinced that our mind, as a part of nature, is precharged or preloaded to appreciate the golden mean. :)

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